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Simplifying 8x2 + -16x + 12 = 7 Reorder the terms: 12 + -16x + 8x2 = 7 Solving 12 + -16x + 8x2 = 7 Solving for variable 'x'. Reorder the terms: 12 + -7 + -16x + 8x2 = 7 + -7 Combine like terms: 12 + -7 = 5 5 + -16x + 8x2 = 7 + -7 Combine like terms: 7 + -7 = 0 5 + -16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -2x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -2x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -2x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -2x + x2 = 0 + -0.625 -2x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -2x + x2 = -0.625 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 = -0.625 + 1 Reorder the terms: 1 + -2x + x2 = -0.625 + 1 Combine like terms: -0.625 + 1 = 0.375 1 + -2x + x2 = 0.375 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (x + -1) equal to 0.612372436 and -0.612372436.Subproblem 1
x + -1 = 0.612372436 Simplifying x + -1 = 0.612372436 Reorder the terms: -1 + x = 0.612372436 Solving -1 + x = 0.612372436 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 = 0.612372436 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.612372436 + 1 x = 0.612372436 + 1 Combine like terms: 0.612372436 + 1 = 1.612372436 x = 1.612372436 Simplifying x = 1.612372436Subproblem 2
x + -1 = -0.612372436 Simplifying x + -1 = -0.612372436 Reorder the terms: -1 + x = -0.612372436 Solving -1 + x = -0.612372436 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 = -0.612372436 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.612372436 + 1 x = -0.612372436 + 1 Combine like terms: -0.612372436 + 1 = 0.387627564 x = 0.387627564 Simplifying x = 0.387627564Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.612372436, 0.387627564}
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