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Simplifying (-6x2 + -5x + 4) + -1(-4x2 + 7x + -8) = 0 Reorder the terms: (4 + -5x + -6x2) + -1(-4x2 + 7x + -8) = 0 Remove parenthesis around (4 + -5x + -6x2) 4 + -5x + -6x2 + -1(-4x2 + 7x + -8) = 0 Reorder the terms: 4 + -5x + -6x2 + -1(-8 + 7x + -4x2) = 0 4 + -5x + -6x2 + (-8 * -1 + 7x * -1 + -4x2 * -1) = 0 4 + -5x + -6x2 + (8 + -7x + 4x2) = 0 Reorder the terms: 4 + 8 + -5x + -7x + -6x2 + 4x2 = 0 Combine like terms: 4 + 8 = 12 12 + -5x + -7x + -6x2 + 4x2 = 0 Combine like terms: -5x + -7x = -12x 12 + -12x + -6x2 + 4x2 = 0 Combine like terms: -6x2 + 4x2 = -2x2 12 + -12x + -2x2 = 0 Solving 12 + -12x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 6 + -6x + -1x2 = 0 Solving 6 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + 6x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 6x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 6x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6x + x2 = 0 + 6 6x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 6x + x2 = 6 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 6 + 9 Reorder the terms: 9 + 6x + x2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + 6x + x2 = 15 Factor a perfect square on the left side: (x + 3)(x + 3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 3) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 3 = 3.872983346 Simplifying x + 3 = 3.872983346 Reorder the terms: 3 + x = 3.872983346 Solving 3 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.872983346 + -3 x = 3.872983346 + -3 Combine like terms: 3.872983346 + -3 = 0.872983346 x = 0.872983346 Simplifying x = 0.872983346Subproblem 2
x + 3 = -3.872983346 Simplifying x + 3 = -3.872983346 Reorder the terms: 3 + x = -3.872983346 Solving 3 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.872983346 + -3 x = -3.872983346 + -3 Combine like terms: -3.872983346 + -3 = -6.872983346 x = -6.872983346 Simplifying x = -6.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.872983346, -6.872983346}Solution
x = {0.872983346, -6.872983346}
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