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Simplifying 2x(2x + -1x + 2) = 5x + 20 + 10 Reorder the terms: 2x(2 + 2x + -1x) = 5x + 20 + 10 Combine like terms: 2x + -1x = 1x 2x(2 + 1x) = 5x + 20 + 10 (2 * 2x + 1x * 2x) = 5x + 20 + 10 (4x + 2x2) = 5x + 20 + 10 Reorder the terms: 4x + 2x2 = 20 + 10 + 5x Combine like terms: 20 + 10 = 30 4x + 2x2 = 30 + 5x Solving 4x + 2x2 = 30 + 5x Solving for variable 'x'. Reorder the terms: -30 + 4x + -5x + 2x2 = 30 + 5x + -30 + -5x Combine like terms: 4x + -5x = -1x -30 + -1x + 2x2 = 30 + 5x + -30 + -5x Reorder the terms: -30 + -1x + 2x2 = 30 + -30 + 5x + -5x Combine like terms: 30 + -30 = 0 -30 + -1x + 2x2 = 0 + 5x + -5x -30 + -1x + 2x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -30 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15 + -0.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -0.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -0.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -0.5x + x2 = 0 + 15 -0.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -0.5x + x2 = 15 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 15 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 15 + 0.0625 Combine like terms: 15 + 0.0625 = 15.0625 0.0625 + -0.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + -0.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x + -0.25 = 3.881043674 Simplifying x + -0.25 = 3.881043674 Reorder the terms: -0.25 + x = 3.881043674 Solving -0.25 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 3.881043674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.881043674 + 0.25 x = 3.881043674 + 0.25 Combine like terms: 3.881043674 + 0.25 = 4.131043674 x = 4.131043674 Simplifying x = 4.131043674Subproblem 2
x + -0.25 = -3.881043674 Simplifying x + -0.25 = -3.881043674 Reorder the terms: -0.25 + x = -3.881043674 Solving -0.25 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -3.881043674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.881043674 + 0.25 x = -3.881043674 + 0.25 Combine like terms: -3.881043674 + 0.25 = -3.631043674 x = -3.631043674 Simplifying x = -3.631043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.131043674, -3.631043674}
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