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Simplifying 3x2 + -5 + -14x2 + 13 + 8x = 0 Reorder the terms: -5 + 13 + 8x + 3x2 + -14x2 = 0 Combine like terms: -5 + 13 = 8 8 + 8x + 3x2 + -14x2 = 0 Combine like terms: 3x2 + -14x2 = -11x2 8 + 8x + -11x2 = 0 Solving 8 + 8x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.7272727273 + -0.7272727273x + x2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + -0.7272727273x + 0.7272727273 + x2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + -0.7272727273x + x2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + -0.7272727273x + x2 = 0 + 0.7272727273 -0.7272727273x + x2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 -0.7272727273x + x2 = 0.7272727273 The x term is -0.7272727273x. Take half its coefficient (-0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. -0.7272727273x + 0.1322314050 + x2 = 0.7272727273 + 0.1322314050 Reorder the terms: 0.1322314050 + -0.7272727273x + x2 = 0.7272727273 + 0.1322314050 Combine like terms: 0.7272727273 + 0.1322314050 = 0.8595041323 0.1322314050 + -0.7272727273x + x2 = 0.8595041323 Factor a perfect square on the left side: (x + -0.3636363637)(x + -0.3636363637) = 0.8595041323 Calculate the square root of the right side: 0.927094457 Break this problem into two subproblems by setting (x + -0.3636363637) equal to 0.927094457 and -0.927094457.Subproblem 1
x + -0.3636363637 = 0.927094457 Simplifying x + -0.3636363637 = 0.927094457 Reorder the terms: -0.3636363637 + x = 0.927094457 Solving -0.3636363637 + x = 0.927094457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = 0.927094457 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = 0.927094457 + 0.3636363637 x = 0.927094457 + 0.3636363637 Combine like terms: 0.927094457 + 0.3636363637 = 1.2907308207 x = 1.2907308207 Simplifying x = 1.2907308207Subproblem 2
x + -0.3636363637 = -0.927094457 Simplifying x + -0.3636363637 = -0.927094457 Reorder the terms: -0.3636363637 + x = -0.927094457 Solving -0.3636363637 + x = -0.927094457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = -0.927094457 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = -0.927094457 + 0.3636363637 x = -0.927094457 + 0.3636363637 Combine like terms: -0.927094457 + 0.3636363637 = -0.5634580933 x = -0.5634580933 Simplifying x = -0.5634580933Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2907308207, -0.5634580933}
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