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Simplifying x(4x + 2) = 13 Reorder the terms: x(2 + 4x) = 13 (2 * x + 4x * x) = 13 (2x + 4x2) = 13 Solving 2x + 4x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 2x + 4x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 0.5x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 0.5x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 0.5x + x2 = 0 + 3.25 0.5x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 0.5x + x2 = 3.25 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 = 3.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 3.25 + 0.0625 Combine like terms: 3.25 + 0.0625 = 3.3125 0.0625 + 0.5x + x2 = 3.3125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (x + 0.25) equal to 1.820027472 and -1.820027472.Subproblem 1
x + 0.25 = 1.820027472 Simplifying x + 0.25 = 1.820027472 Reorder the terms: 0.25 + x = 1.820027472 Solving 0.25 + x = 1.820027472 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 = 1.820027472 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.820027472 + -0.25 x = 1.820027472 + -0.25 Combine like terms: 1.820027472 + -0.25 = 1.570027472 x = 1.570027472 Simplifying x = 1.570027472Subproblem 2
x + 0.25 = -1.820027472 Simplifying x + 0.25 = -1.820027472 Reorder the terms: 0.25 + x = -1.820027472 Solving 0.25 + x = -1.820027472 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 = -1.820027472 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.820027472 + -0.25 x = -1.820027472 + -0.25 Combine like terms: -1.820027472 + -0.25 = -2.070027472 x = -2.070027472 Simplifying x = -2.070027472Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.570027472, -2.070027472}
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