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Simplifying 4x2 + 6x + -13 = 0 Reorder the terms: -13 + 6x + 4x2 = 0 Solving -13 + 6x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 1.5x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 1.5x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 1.5x + x2 = 0 + 3.25 1.5x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 1.5x + x2 = 3.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 3.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 3.25 + 0.5625 Combine like terms: 3.25 + 0.5625 = 3.8125 0.5625 + 1.5x + x2 = 3.8125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (x + 0.75) equal to 1.952562419 and -1.952562419.Subproblem 1
x + 0.75 = 1.952562419 Simplifying x + 0.75 = 1.952562419 Reorder the terms: 0.75 + x = 1.952562419 Solving 0.75 + x = 1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.952562419 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.952562419 + -0.75 x = 1.952562419 + -0.75 Combine like terms: 1.952562419 + -0.75 = 1.202562419 x = 1.202562419 Simplifying x = 1.202562419Subproblem 2
x + 0.75 = -1.952562419 Simplifying x + 0.75 = -1.952562419 Reorder the terms: 0.75 + x = -1.952562419 Solving 0.75 + x = -1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.952562419 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.952562419 + -0.75 x = -1.952562419 + -0.75 Combine like terms: -1.952562419 + -0.75 = -2.702562419 x = -2.702562419 Simplifying x = -2.702562419Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.202562419, -2.702562419}
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