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Simplifying 32x2 + -5x + -7 = 0 Reorder the terms: -7 + -5x + 32x2 = 0 Solving -7 + -5x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.21875 + -0.15625x + x2 = 0 Move the constant term to the right: Add '0.21875' to each side of the equation. -0.21875 + -0.15625x + 0.21875 + x2 = 0 + 0.21875 Reorder the terms: -0.21875 + 0.21875 + -0.15625x + x2 = 0 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + -0.15625x + x2 = 0 + 0.21875 -0.15625x + x2 = 0 + 0.21875 Combine like terms: 0 + 0.21875 = 0.21875 -0.15625x + x2 = 0.21875 The x term is -0.15625x. Take half its coefficient (-0.078125). Square it (0.006103515625) and add it to both sides. Add '0.006103515625' to each side of the equation. -0.15625x + 0.006103515625 + x2 = 0.21875 + 0.006103515625 Reorder the terms: 0.006103515625 + -0.15625x + x2 = 0.21875 + 0.006103515625 Combine like terms: 0.21875 + 0.006103515625 = 0.224853515625 0.006103515625 + -0.15625x + x2 = 0.224853515625 Factor a perfect square on the left side: (x + -0.078125)(x + -0.078125) = 0.224853515625 Calculate the square root of the right side: 0.474187216 Break this problem into two subproblems by setting (x + -0.078125) equal to 0.474187216 and -0.474187216.Subproblem 1
x + -0.078125 = 0.474187216 Simplifying x + -0.078125 = 0.474187216 Reorder the terms: -0.078125 + x = 0.474187216 Solving -0.078125 + x = 0.474187216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.078125' to each side of the equation. -0.078125 + 0.078125 + x = 0.474187216 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + x = 0.474187216 + 0.078125 x = 0.474187216 + 0.078125 Combine like terms: 0.474187216 + 0.078125 = 0.552312216 x = 0.552312216 Simplifying x = 0.552312216Subproblem 2
x + -0.078125 = -0.474187216 Simplifying x + -0.078125 = -0.474187216 Reorder the terms: -0.078125 + x = -0.474187216 Solving -0.078125 + x = -0.474187216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.078125' to each side of the equation. -0.078125 + 0.078125 + x = -0.474187216 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + x = -0.474187216 + 0.078125 x = -0.474187216 + 0.078125 Combine like terms: -0.474187216 + 0.078125 = -0.396062216 x = -0.396062216 Simplifying x = -0.396062216Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.552312216, -0.396062216}
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