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Simplifying 4x2 + 5x = 13 Reorder the terms: 5x + 4x2 = 13 Solving 5x + 4x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 5x + 4x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 1.25x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 1.25x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 1.25x + x2 = 0 + 3.25 1.25x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 1.25x + x2 = 3.25 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 3.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 3.25 + 0.390625 Combine like terms: 3.25 + 0.390625 = 3.640625 0.390625 + 1.25x + x2 = 3.640625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 3.640625 Calculate the square root of the right side: 1.90804219 Break this problem into two subproblems by setting (x + 0.625) equal to 1.90804219 and -1.90804219.Subproblem 1
x + 0.625 = 1.90804219 Simplifying x + 0.625 = 1.90804219 Reorder the terms: 0.625 + x = 1.90804219 Solving 0.625 + x = 1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.90804219 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.90804219 + -0.625 x = 1.90804219 + -0.625 Combine like terms: 1.90804219 + -0.625 = 1.28304219 x = 1.28304219 Simplifying x = 1.28304219Subproblem 2
x + 0.625 = -1.90804219 Simplifying x + 0.625 = -1.90804219 Reorder the terms: 0.625 + x = -1.90804219 Solving 0.625 + x = -1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.90804219 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.90804219 + -0.625 x = -1.90804219 + -0.625 Combine like terms: -1.90804219 + -0.625 = -2.53304219 x = -2.53304219 Simplifying x = -2.53304219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.28304219, -2.53304219}
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