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Simplifying 5x + -7(2x + -3) + 15 = 4(5x + -8) * 9x + -12 Reorder the terms: 5x + -7(-3 + 2x) + 15 = 4(5x + -8) * 9x + -12 5x + (-3 * -7 + 2x * -7) + 15 = 4(5x + -8) * 9x + -12 5x + (21 + -14x) + 15 = 4(5x + -8) * 9x + -12 Reorder the terms: 21 + 15 + 5x + -14x = 4(5x + -8) * 9x + -12 Combine like terms: 21 + 15 = 36 36 + 5x + -14x = 4(5x + -8) * 9x + -12 Combine like terms: 5x + -14x = -9x 36 + -9x = 4(5x + -8) * 9x + -12 Reorder the terms: 36 + -9x = 4(-8 + 5x) * 9x + -12 Reorder the terms for easier multiplication: 36 + -9x = 4 * 9x(-8 + 5x) + -12 Multiply 4 * 9 36 + -9x = 36x(-8 + 5x) + -12 36 + -9x = (-8 * 36x + 5x * 36x) + -12 36 + -9x = (-288x + 180x2) + -12 Reorder the terms: 36 + -9x = -12 + -288x + 180x2 Solving 36 + -9x = -12 + -288x + 180x2 Solving for variable 'x'. Reorder the terms: 36 + 12 + -9x + 288x + -180x2 = -12 + -288x + 180x2 + 12 + 288x + -180x2 Combine like terms: 36 + 12 = 48 48 + -9x + 288x + -180x2 = -12 + -288x + 180x2 + 12 + 288x + -180x2 Combine like terms: -9x + 288x = 279x 48 + 279x + -180x2 = -12 + -288x + 180x2 + 12 + 288x + -180x2 Reorder the terms: 48 + 279x + -180x2 = -12 + 12 + -288x + 288x + 180x2 + -180x2 Combine like terms: -12 + 12 = 0 48 + 279x + -180x2 = 0 + -288x + 288x + 180x2 + -180x2 48 + 279x + -180x2 = -288x + 288x + 180x2 + -180x2 Combine like terms: -288x + 288x = 0 48 + 279x + -180x2 = 0 + 180x2 + -180x2 48 + 279x + -180x2 = 180x2 + -180x2 Combine like terms: 180x2 + -180x2 = 0 48 + 279x + -180x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(16 + 93x + -60x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(16 + 93x + -60x2)' equal to zero and attempt to solve: Simplifying 16 + 93x + -60x2 = 0 Solving 16 + 93x + -60x2 = 0 Begin completing the square. Divide all terms by -60 the coefficient of the squared term: Divide each side by '-60'. -0.2666666667 + -1.55x + x2 = 0.0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + -1.55x + 0.2666666667 + x2 = 0.0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + -1.55x + x2 = 0.0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + -1.55x + x2 = 0.0 + 0.2666666667 -1.55x + x2 = 0.0 + 0.2666666667 Combine like terms: 0.0 + 0.2666666667 = 0.2666666667 -1.55x + x2 = 0.2666666667 The x term is -1.55x. Take half its coefficient (-0.775). Square it (0.600625) and add it to both sides. Add '0.600625' to each side of the equation. -1.55x + 0.600625 + x2 = 0.2666666667 + 0.600625 Reorder the terms: 0.600625 + -1.55x + x2 = 0.2666666667 + 0.600625 Combine like terms: 0.2666666667 + 0.600625 = 0.8672916667 0.600625 + -1.55x + x2 = 0.8672916667 Factor a perfect square on the left side: (x + -0.775)(x + -0.775) = 0.8672916667 Calculate the square root of the right side: 0.931284955 Break this problem into two subproblems by setting (x + -0.775) equal to 0.931284955 and -0.931284955.Subproblem 1
x + -0.775 = 0.931284955 Simplifying x + -0.775 = 0.931284955 Reorder the terms: -0.775 + x = 0.931284955 Solving -0.775 + x = 0.931284955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.775' to each side of the equation. -0.775 + 0.775 + x = 0.931284955 + 0.775 Combine like terms: -0.775 + 0.775 = 0.000 0.000 + x = 0.931284955 + 0.775 x = 0.931284955 + 0.775 Combine like terms: 0.931284955 + 0.775 = 1.706284955 x = 1.706284955 Simplifying x = 1.706284955Subproblem 2
x + -0.775 = -0.931284955 Simplifying x + -0.775 = -0.931284955 Reorder the terms: -0.775 + x = -0.931284955 Solving -0.775 + x = -0.931284955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.775' to each side of the equation. -0.775 + 0.775 + x = -0.931284955 + 0.775 Combine like terms: -0.775 + 0.775 = 0.000 0.000 + x = -0.931284955 + 0.775 x = -0.931284955 + 0.775 Combine like terms: -0.931284955 + 0.775 = -0.156284955 x = -0.156284955 Simplifying x = -0.156284955Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.706284955, -0.156284955}Solution
x = {1.706284955, -0.156284955}
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