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Simplifying 16x2 + 80x = 70 Reorder the terms: 80x + 16x2 = 70 Solving 80x + 16x2 = 70 Solving for variable 'x'. Reorder the terms: -70 + 80x + 16x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + 80x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 40x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + 40x + 8x2)' equal to zero and attempt to solve: Simplifying -35 + 40x + 8x2 = 0 Solving -35 + 40x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + 5x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 5x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 5x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 5x + x2 = 0 + 4.375 5x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 5x + x2 = 4.375 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 = 4.375 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 4.375 + 6.25 Combine like terms: 4.375 + 6.25 = 10.625 6.25 + 5x + x2 = 10.625 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 10.625 Calculate the square root of the right side: 3.259601203 Break this problem into two subproblems by setting (x + 2.5) equal to 3.259601203 and -3.259601203.Subproblem 1
x + 2.5 = 3.259601203 Simplifying x + 2.5 = 3.259601203 Reorder the terms: 2.5 + x = 3.259601203 Solving 2.5 + x = 3.259601203 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 = 3.259601203 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.259601203 + -2.5 x = 3.259601203 + -2.5 Combine like terms: 3.259601203 + -2.5 = 0.759601203 x = 0.759601203 Simplifying x = 0.759601203Subproblem 2
x + 2.5 = -3.259601203 Simplifying x + 2.5 = -3.259601203 Reorder the terms: 2.5 + x = -3.259601203 Solving 2.5 + x = -3.259601203 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 = -3.259601203 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.259601203 + -2.5 x = -3.259601203 + -2.5 Combine like terms: -3.259601203 + -2.5 = -5.759601203 x = -5.759601203 Simplifying x = -5.759601203Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.759601203, -5.759601203}Solution
x = {0.759601203, -5.759601203}
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