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Simplifying 8x = 2x2 + 3 Reorder the terms: 8x = 3 + 2x2 Solving 8x = 3 + 2x2 Solving for variable 'x'. Reorder the terms: -3 + 8x + -2x2 = 3 + 2x2 + -3 + -2x2 Reorder the terms: -3 + 8x + -2x2 = 3 + -3 + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 -3 + 8x + -2x2 = 0 + 2x2 + -2x2 -3 + 8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -3 + 8x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -4x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4x + x2 = 0 + -1.5 -4x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4x + x2 = -1.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -1.5 + 4 Reorder the terms: 4 + -4x + x2 = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 4 + -4x + x2 = 2.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x + -2) equal to 1.58113883 and -1.58113883.Subproblem 1
x + -2 = 1.58113883 Simplifying x + -2 = 1.58113883 Reorder the terms: -2 + x = 1.58113883 Solving -2 + x = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.58113883 + 2 x = 1.58113883 + 2 Combine like terms: 1.58113883 + 2 = 3.58113883 x = 3.58113883 Simplifying x = 3.58113883Subproblem 2
x + -2 = -1.58113883 Simplifying x + -2 = -1.58113883 Reorder the terms: -2 + x = -1.58113883 Solving -2 + x = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.58113883 + 2 x = -1.58113883 + 2 Combine like terms: -1.58113883 + 2 = 0.41886117 x = 0.41886117 Simplifying x = 0.41886117Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.58113883, 0.41886117}
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