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Simplifying 4x2 + -24x + -30 = 0 Reorder the terms: -30 + -24x + 4x2 = 0 Solving -30 + -24x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying -15 + -12x + 2x2 = 0 Solving -15 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -6x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -6x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -6x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -6x + x2 = 0 + 7.5 -6x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -6x + x2 = 7.5 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 = 7.5 + 9 Reorder the terms: 9 + -6x + x2 = 7.5 + 9 Combine like terms: 7.5 + 9 = 16.5 9 + -6x + x2 = 16.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (x + -3) equal to 4.062019202 and -4.062019202.Subproblem 1
x + -3 = 4.062019202 Simplifying x + -3 = 4.062019202 Reorder the terms: -3 + x = 4.062019202 Solving -3 + x = 4.062019202 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 = 4.062019202 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.062019202 + 3 x = 4.062019202 + 3 Combine like terms: 4.062019202 + 3 = 7.062019202 x = 7.062019202 Simplifying x = 7.062019202Subproblem 2
x + -3 = -4.062019202 Simplifying x + -3 = -4.062019202 Reorder the terms: -3 + x = -4.062019202 Solving -3 + x = -4.062019202 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 = -4.062019202 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.062019202 + 3 x = -4.062019202 + 3 Combine like terms: -4.062019202 + 3 = -1.062019202 x = -1.062019202 Simplifying x = -1.062019202Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.062019202, -1.062019202}Solution
x = {7.062019202, -1.062019202}
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