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Simplifying -4x2 + 60x + 900 = 0 Reorder the terms: 900 + 60x + -4x2 = 0 Solving 900 + 60x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(225 + 15x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(225 + 15x + -1x2)' equal to zero and attempt to solve: Simplifying 225 + 15x + -1x2 = 0 Solving 225 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -225 + -15x + x2 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + -15x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + -15x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + -15x + x2 = 0 + 225 -15x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 -15x + x2 = 225 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 = 225 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 225 + 56.25 Combine like terms: 225 + 56.25 = 281.25 56.25 + -15x + x2 = 281.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 281.25 Calculate the square root of the right side: 16.770509831 Break this problem into two subproblems by setting (x + -7.5) equal to 16.770509831 and -16.770509831.Subproblem 1
x + -7.5 = 16.770509831 Simplifying x + -7.5 = 16.770509831 Reorder the terms: -7.5 + x = 16.770509831 Solving -7.5 + x = 16.770509831 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 = 16.770509831 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 16.770509831 + 7.5 x = 16.770509831 + 7.5 Combine like terms: 16.770509831 + 7.5 = 24.270509831 x = 24.270509831 Simplifying x = 24.270509831Subproblem 2
x + -7.5 = -16.770509831 Simplifying x + -7.5 = -16.770509831 Reorder the terms: -7.5 + x = -16.770509831 Solving -7.5 + x = -16.770509831 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 = -16.770509831 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -16.770509831 + 7.5 x = -16.770509831 + 7.5 Combine like terms: -16.770509831 + 7.5 = -9.270509831 x = -9.270509831 Simplifying x = -9.270509831Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.270509831, -9.270509831}Solution
x = {24.270509831, -9.270509831}
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