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Simplifying -16x2 + 50x + 120 = 0 Reorder the terms: 120 + 50x + -16x2 = 0 Solving 120 + 50x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(60 + 25x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + 25x + -8x2)' equal to zero and attempt to solve: Simplifying 60 + 25x + -8x2 = 0 Solving 60 + 25x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -7.5 + -3.125x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -3.125x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -3.125x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -3.125x + x2 = 0 + 7.5 -3.125x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -3.125x + x2 = 7.5 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 7.5 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 7.5 + 2.44140625 Combine like terms: 7.5 + 2.44140625 = 9.94140625 2.44140625 + -3.125x + x2 = 9.94140625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 9.94140625 Calculate the square root of the right side: 3.152999564 Break this problem into two subproblems by setting (x + -1.5625) equal to 3.152999564 and -3.152999564.Subproblem 1
x + -1.5625 = 3.152999564 Simplifying x + -1.5625 = 3.152999564 Reorder the terms: -1.5625 + x = 3.152999564 Solving -1.5625 + x = 3.152999564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 3.152999564 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 3.152999564 + 1.5625 x = 3.152999564 + 1.5625 Combine like terms: 3.152999564 + 1.5625 = 4.715499564 x = 4.715499564 Simplifying x = 4.715499564Subproblem 2
x + -1.5625 = -3.152999564 Simplifying x + -1.5625 = -3.152999564 Reorder the terms: -1.5625 + x = -3.152999564 Solving -1.5625 + x = -3.152999564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -3.152999564 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -3.152999564 + 1.5625 x = -3.152999564 + 1.5625 Combine like terms: -3.152999564 + 1.5625 = -1.590499564 x = -1.590499564 Simplifying x = -1.590499564Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.715499564, -1.590499564}Solution
x = {4.715499564, -1.590499564}
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