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Simplifying 8x2 + -28x + 2x + -7 = 0.5 Reorder the terms: -7 + -28x + 2x + 8x2 = 0.5 Combine like terms: -28x + 2x = -26x -7 + -26x + 8x2 = 0.5 Solving -7 + -26x + 8x2 = 0.5 Solving for variable 'x'. Reorder the terms: -7 + -0.5 + -26x + 8x2 = 0.5 + -0.5 Combine like terms: -7 + -0.5 = -7.5 -7.5 + -26x + 8x2 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -7.5 + -26x + 8x2 = 0.0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.9375 + -3.25x + x2 = 0.0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -3.25x + 0.9375 + x2 = 0.0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -3.25x + x2 = 0.0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -3.25x + x2 = 0.0 + 0.9375 -3.25x + x2 = 0.0 + 0.9375 Combine like terms: 0.0 + 0.9375 = 0.9375 -3.25x + x2 = 0.9375 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 0.9375 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 0.9375 + 2.640625 Combine like terms: 0.9375 + 2.640625 = 3.578125 2.640625 + -3.25x + x2 = 3.578125 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 3.578125 Calculate the square root of the right side: 1.891593244 Break this problem into two subproblems by setting (x + -1.625) equal to 1.891593244 and -1.891593244.Subproblem 1
x + -1.625 = 1.891593244 Simplifying x + -1.625 = 1.891593244 Reorder the terms: -1.625 + x = 1.891593244 Solving -1.625 + x = 1.891593244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.891593244 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.891593244 + 1.625 x = 1.891593244 + 1.625 Combine like terms: 1.891593244 + 1.625 = 3.516593244 x = 3.516593244 Simplifying x = 3.516593244Subproblem 2
x + -1.625 = -1.891593244 Simplifying x + -1.625 = -1.891593244 Reorder the terms: -1.625 + x = -1.891593244 Solving -1.625 + x = -1.891593244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.891593244 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.891593244 + 1.625 x = -1.891593244 + 1.625 Combine like terms: -1.891593244 + 1.625 = -0.266593244 x = -0.266593244 Simplifying x = -0.266593244Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.516593244, -0.266593244}
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