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Simplifying -16x2 + 100x + 120 = 0 Reorder the terms: 120 + 100x + -16x2 = 0 Solving 120 + 100x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(30 + 25x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(30 + 25x + -4x2)' equal to zero and attempt to solve: Simplifying 30 + 25x + -4x2 = 0 Solving 30 + 25x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -7.5 + -6.25x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -6.25x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -6.25x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -6.25x + x2 = 0 + 7.5 -6.25x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -6.25x + x2 = 7.5 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 7.5 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 7.5 + 9.765625 Combine like terms: 7.5 + 9.765625 = 17.265625 9.765625 + -6.25x + x2 = 17.265625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 17.265625 Calculate the square root of the right side: 4.155192535 Break this problem into two subproblems by setting (x + -3.125) equal to 4.155192535 and -4.155192535.Subproblem 1
x + -3.125 = 4.155192535 Simplifying x + -3.125 = 4.155192535 Reorder the terms: -3.125 + x = 4.155192535 Solving -3.125 + x = 4.155192535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 4.155192535 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 4.155192535 + 3.125 x = 4.155192535 + 3.125 Combine like terms: 4.155192535 + 3.125 = 7.280192535 x = 7.280192535 Simplifying x = 7.280192535Subproblem 2
x + -3.125 = -4.155192535 Simplifying x + -3.125 = -4.155192535 Reorder the terms: -3.125 + x = -4.155192535 Solving -3.125 + x = -4.155192535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -4.155192535 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -4.155192535 + 3.125 x = -4.155192535 + 3.125 Combine like terms: -4.155192535 + 3.125 = -1.030192535 x = -1.030192535 Simplifying x = -1.030192535Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.280192535, -1.030192535}Solution
x = {7.280192535, -1.030192535}
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