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Simplifying -16x2 + 240x + 2400 = 0 Reorder the terms: 2400 + 240x + -16x2 = 0 Solving 2400 + 240x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(150 + 15x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(150 + 15x + -1x2)' equal to zero and attempt to solve: Simplifying 150 + 15x + -1x2 = 0 Solving 150 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -150 + -15x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + -15x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -15x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -15x + x2 = 0 + 150 -15x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -15x + x2 = 150 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 150 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 150 + 56.25 Combine like terms: 150 + 56.25 = 206.25 56.25 + -15x + x2 = 206.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 206.25 Calculate the square root of the right side: 14.361406616 Break this problem into two subproblems by setting (x + -7.5) equal to 14.361406616 and -14.361406616.Subproblem 1
x + -7.5 = 14.361406616 Simplifying x + -7.5 = 14.361406616 Reorder the terms: -7.5 + x = 14.361406616 Solving -7.5 + x = 14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 14.361406616 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 14.361406616 + 7.5 x = 14.361406616 + 7.5 Combine like terms: 14.361406616 + 7.5 = 21.861406616 x = 21.861406616 Simplifying x = 21.861406616Subproblem 2
x + -7.5 = -14.361406616 Simplifying x + -7.5 = -14.361406616 Reorder the terms: -7.5 + x = -14.361406616 Solving -7.5 + x = -14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -14.361406616 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -14.361406616 + 7.5 x = -14.361406616 + 7.5 Combine like terms: -14.361406616 + 7.5 = -6.861406616 x = -6.861406616 Simplifying x = -6.861406616Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.861406616, -6.861406616}Solution
x = {21.861406616, -6.861406616}
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