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Simplifying 5x2 + -11x + 3 + -6x + -13x2 = 0 Reorder the terms: 3 + -11x + -6x + 5x2 + -13x2 = 0 Combine like terms: -11x + -6x = -17x 3 + -17x + 5x2 + -13x2 = 0 Combine like terms: 5x2 + -13x2 = -8x2 3 + -17x + -8x2 = 0 Solving 3 + -17x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + 2.125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 2.125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 2.125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 2.125x + x2 = 0 + 0.375 2.125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 2.125x + x2 = 0.375 The x term is 2.125x. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125x + 1.12890625 + x2 = 0.375 + 1.12890625 Reorder the terms: 1.12890625 + 2.125x + x2 = 0.375 + 1.12890625 Combine like terms: 0.375 + 1.12890625 = 1.50390625 1.12890625 + 2.125x + x2 = 1.50390625 Factor a perfect square on the left side: (x + 1.0625)(x + 1.0625) = 1.50390625 Calculate the square root of the right side: 1.226338554 Break this problem into two subproblems by setting (x + 1.0625) equal to 1.226338554 and -1.226338554.Subproblem 1
x + 1.0625 = 1.226338554 Simplifying x + 1.0625 = 1.226338554 Reorder the terms: 1.0625 + x = 1.226338554 Solving 1.0625 + x = 1.226338554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = 1.226338554 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = 1.226338554 + -1.0625 x = 1.226338554 + -1.0625 Combine like terms: 1.226338554 + -1.0625 = 0.163838554 x = 0.163838554 Simplifying x = 0.163838554Subproblem 2
x + 1.0625 = -1.226338554 Simplifying x + 1.0625 = -1.226338554 Reorder the terms: 1.0625 + x = -1.226338554 Solving 1.0625 + x = -1.226338554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = -1.226338554 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = -1.226338554 + -1.0625 x = -1.226338554 + -1.0625 Combine like terms: -1.226338554 + -1.0625 = -2.288838554 x = -2.288838554 Simplifying x = -2.288838554Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.163838554, -2.288838554}
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