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Simplifying 59x = 8x2 + -20 Reorder the terms: 59x = -20 + 8x2 Solving 59x = -20 + 8x2 Solving for variable 'x'. Reorder the terms: 20 + 59x + -8x2 = -20 + 8x2 + 20 + -8x2 Reorder the terms: 20 + 59x + -8x2 = -20 + 20 + 8x2 + -8x2 Combine like terms: -20 + 20 = 0 20 + 59x + -8x2 = 0 + 8x2 + -8x2 20 + 59x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 20 + 59x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.5 + -7.375x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -7.375x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -7.375x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -7.375x + x2 = 0 + 2.5 -7.375x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -7.375x + x2 = 2.5 The x term is -7.375x. Take half its coefficient (-3.6875). Square it (13.59765625) and add it to both sides. Add '13.59765625' to each side of the equation. -7.375x + 13.59765625 + x2 = 2.5 + 13.59765625 Reorder the terms: 13.59765625 + -7.375x + x2 = 2.5 + 13.59765625 Combine like terms: 2.5 + 13.59765625 = 16.09765625 13.59765625 + -7.375x + x2 = 16.09765625 Factor a perfect square on the left side: (x + -3.6875)(x + -3.6875) = 16.09765625 Calculate the square root of the right side: 4.012188461 Break this problem into two subproblems by setting (x + -3.6875) equal to 4.012188461 and -4.012188461.Subproblem 1
x + -3.6875 = 4.012188461 Simplifying x + -3.6875 = 4.012188461 Reorder the terms: -3.6875 + x = 4.012188461 Solving -3.6875 + x = 4.012188461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + x = 4.012188461 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + x = 4.012188461 + 3.6875 x = 4.012188461 + 3.6875 Combine like terms: 4.012188461 + 3.6875 = 7.699688461 x = 7.699688461 Simplifying x = 7.699688461Subproblem 2
x + -3.6875 = -4.012188461 Simplifying x + -3.6875 = -4.012188461 Reorder the terms: -3.6875 + x = -4.012188461 Solving -3.6875 + x = -4.012188461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + x = -4.012188461 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + x = -4.012188461 + 3.6875 x = -4.012188461 + 3.6875 Combine like terms: -4.012188461 + 3.6875 = -0.324688461 x = -0.324688461 Simplifying x = -0.324688461Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.699688461, -0.324688461}
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