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Simplifying 16x(5 + -1x) = 30 (5 * 16x + -1x * 16x) = 30 (80x + -16x2) = 30 Solving 80x + -16x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 80x + -16x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 80x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 40x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 40x + -8x2)' equal to zero and attempt to solve: Simplifying -15 + 40x + -8x2 = 0 Solving -15 + 40x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.875 + -5x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -5x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -5x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -5x + x2 = 0 + -1.875 -5x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -5x + x2 = -1.875 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -1.875 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.875 + 6.25 Combine like terms: -1.875 + 6.25 = 4.375 6.25 + -5x + x2 = 4.375 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.375 Calculate the square root of the right side: 2.091650066 Break this problem into two subproblems by setting (x + -2.5) equal to 2.091650066 and -2.091650066.Subproblem 1
x + -2.5 = 2.091650066 Simplifying x + -2.5 = 2.091650066 Reorder the terms: -2.5 + x = 2.091650066 Solving -2.5 + x = 2.091650066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.091650066 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.091650066 + 2.5 x = 2.091650066 + 2.5 Combine like terms: 2.091650066 + 2.5 = 4.591650066 x = 4.591650066 Simplifying x = 4.591650066Subproblem 2
x + -2.5 = -2.091650066 Simplifying x + -2.5 = -2.091650066 Reorder the terms: -2.5 + x = -2.091650066 Solving -2.5 + x = -2.091650066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.091650066 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.091650066 + 2.5 x = -2.091650066 + 2.5 Combine like terms: -2.091650066 + 2.5 = 0.408349934 x = 0.408349934 Simplifying x = 0.408349934Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.591650066, 0.408349934}Solution
x = {4.591650066, 0.408349934}
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