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Simplifying 17x(5x + -4) = 64 Reorder the terms: 17x(-4 + 5x) = 64 (-4 * 17x + 5x * 17x) = 64 (-68x + 85x2) = 64 Solving -68x + 85x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + -68x + 85x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + -68x + 85x2 = 0 Begin completing the square. Divide all terms by 85 the coefficient of the squared term: Divide each side by '85'. -0.7529411765 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.7529411765' to each side of the equation. -0.7529411765 + -0.8x + 0.7529411765 + x2 = 0 + 0.7529411765 Reorder the terms: -0.7529411765 + 0.7529411765 + -0.8x + x2 = 0 + 0.7529411765 Combine like terms: -0.7529411765 + 0.7529411765 = 0.0000000000 0.0000000000 + -0.8x + x2 = 0 + 0.7529411765 -0.8x + x2 = 0 + 0.7529411765 Combine like terms: 0 + 0.7529411765 = 0.7529411765 -0.8x + x2 = 0.7529411765 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.7529411765 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.7529411765 + 0.16 Combine like terms: 0.7529411765 + 0.16 = 0.9129411765 0.16 + -0.8x + x2 = 0.9129411765 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.9129411765 Calculate the square root of the right side: 0.955479553 Break this problem into two subproblems by setting (x + -0.4) equal to 0.955479553 and -0.955479553.Subproblem 1
x + -0.4 = 0.955479553 Simplifying x + -0.4 = 0.955479553 Reorder the terms: -0.4 + x = 0.955479553 Solving -0.4 + x = 0.955479553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.955479553 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.955479553 + 0.4 x = 0.955479553 + 0.4 Combine like terms: 0.955479553 + 0.4 = 1.355479553 x = 1.355479553 Simplifying x = 1.355479553Subproblem 2
x + -0.4 = -0.955479553 Simplifying x + -0.4 = -0.955479553 Reorder the terms: -0.4 + x = -0.955479553 Solving -0.4 + x = -0.955479553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.955479553 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.955479553 + 0.4 x = -0.955479553 + 0.4 Combine like terms: -0.955479553 + 0.4 = -0.555479553 x = -0.555479553 Simplifying x = -0.555479553Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.355479553, -0.555479553}
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