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Simplifying -3x2 + 30x = -120 Reorder the terms: 30x + -3x2 = -120 Solving 30x + -3x2 = -120 Solving for variable 'x'. Reorder the terms: 120 + 30x + -3x2 = -120 + 120 Combine like terms: -120 + 120 = 0 120 + 30x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(40 + 10x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(40 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying 40 + 10x + -1x2 = 0 Solving 40 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + -10x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -10x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -10x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -10x + x2 = 0 + 40 -10x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -10x + x2 = 40 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 40 + 25 Reorder the terms: 25 + -10x + x2 = 40 + 25 Combine like terms: 40 + 25 = 65 25 + -10x + x2 = 65 Factor a perfect square on the left side: (x + -5)(x + -5) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + -5) equal to 8.062257748 and -8.062257748.Subproblem 1
x + -5 = 8.062257748 Simplifying x + -5 = 8.062257748 Reorder the terms: -5 + x = 8.062257748 Solving -5 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 8.062257748 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.062257748 + 5 x = 8.062257748 + 5 Combine like terms: 8.062257748 + 5 = 13.062257748 x = 13.062257748 Simplifying x = 13.062257748Subproblem 2
x + -5 = -8.062257748 Simplifying x + -5 = -8.062257748 Reorder the terms: -5 + x = -8.062257748 Solving -5 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -8.062257748 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.062257748 + 5 x = -8.062257748 + 5 Combine like terms: -8.062257748 + 5 = -3.062257748 x = -3.062257748 Simplifying x = -3.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.062257748, -3.062257748}Solution
x = {13.062257748, -3.062257748}
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