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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 = 2.53304219 x = 2.53304219 Simplifying x = 2.53304219Subproblem 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 = -1.28304219 x = -1.28304219 Simplifying x = -1.28304219Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.53304219, -1.28304219}
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