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Simplifying (8x2) + -16x + -3 = 0 Reorder the terms: -3 + -16x + (8x2) = 0 Solving -3 + -16x + (8x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -2x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -2x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -2x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -2x + x2 = 0 + 0.375 -2x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -2x + x2 = 0.375 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.375 + 1 Reorder the terms: 1 + -2x + x2 = 0.375 + 1 Combine like terms: 0.375 + 1 = 1.375 1 + -2x + x2 = 1.375 Factor a perfect square on the left side: ((x) + -1)((x) + -1) = 1.375 Calculate the square root of the right side: 1.17260394 Break this problem into two subproblems by setting ((x) + -1) equal to 1.17260394 and -1.17260394.Subproblem 1
(x) + -1 = 1.17260394 Simplifying (x) + -1 = 1.17260394 x + -1 = 1.17260394 Reorder the terms: -1 + x = 1.17260394 Solving -1 + x = 1.17260394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.17260394 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.17260394 + 1 x = 1.17260394 + 1 Combine like terms: 1.17260394 + 1 = 2.17260394 x = 2.17260394 Simplifying x = 2.17260394Subproblem 2
(x) + -1 = -1.17260394 Simplifying (x) + -1 = -1.17260394 x + -1 = -1.17260394 Reorder the terms: -1 + x = -1.17260394 Solving -1 + x = -1.17260394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.17260394 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.17260394 + 1 x = -1.17260394 + 1 Combine like terms: -1.17260394 + 1 = -0.17260394 x = -0.17260394 Simplifying x = -0.17260394Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.17260394, -0.17260394}
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