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Simplifying (-3x2 + 5) + -1(5x2 + 2x + -6) = 0 Reorder the terms: (5 + -3x2) + -1(5x2 + 2x + -6) = 0 Remove parenthesis around (5 + -3x2) 5 + -3x2 + -1(5x2 + 2x + -6) = 0 Reorder the terms: 5 + -3x2 + -1(-6 + 2x + 5x2) = 0 5 + -3x2 + (-6 * -1 + 2x * -1 + 5x2 * -1) = 0 5 + -3x2 + (6 + -2x + -5x2) = 0 Reorder the terms: 5 + 6 + -2x + -3x2 + -5x2 = 0 Combine like terms: 5 + 6 = 11 11 + -2x + -3x2 + -5x2 = 0 Combine like terms: -3x2 + -5x2 = -8x2 11 + -2x + -8x2 = 0 Solving 11 + -2x + -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'. -1.375 + 0.25x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 0.25x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 0.25x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 0.25x + x2 = 0 + 1.375 0.25x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 0.25x + x2 = 1.375 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 1.375 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 1.375 + 0.015625 Combine like terms: 1.375 + 0.015625 = 1.390625 0.015625 + 0.25x + x2 = 1.390625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + 0.125) equal to 1.179247642 and -1.179247642.Subproblem 1
x + 0.125 = 1.179247642 Simplifying x + 0.125 = 1.179247642 Reorder the terms: 0.125 + x = 1.179247642 Solving 0.125 + x = 1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.179247642 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.179247642 + -0.125 x = 1.179247642 + -0.125 Combine like terms: 1.179247642 + -0.125 = 1.054247642 x = 1.054247642 Simplifying x = 1.054247642Subproblem 2
x + 0.125 = -1.179247642 Simplifying x + 0.125 = -1.179247642 Reorder the terms: 0.125 + x = -1.179247642 Solving 0.125 + x = -1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.179247642 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.179247642 + -0.125 x = -1.179247642 + -0.125 Combine like terms: -1.179247642 + -0.125 = -1.304247642 x = -1.304247642 Simplifying x = -1.304247642Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.054247642, -1.304247642}
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