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Simplifying 4x2 + -8 = -13x Reorder the terms: -8 + 4x2 = -13x Solving -8 + 4x2 = -13x Solving for variable 'x'. Reorder the terms: -8 + 13x + 4x2 = -13x + 13x Combine like terms: -13x + 13x = 0 -8 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 3.25x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 3.25x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 3.25x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3.25x + x2 = 0 + 2 3.25x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3.25x + x2 = 2 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 2 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 2 + 2.640625 Combine like terms: 2 + 2.640625 = 4.640625 2.640625 + 3.25x + x2 = 4.640625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (x + 1.625) equal to 2.154210992 and -2.154210992.Subproblem 1
x + 1.625 = 2.154210992 Simplifying x + 1.625 = 2.154210992 Reorder the terms: 1.625 + x = 2.154210992 Solving 1.625 + x = 2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 2.154210992 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 2.154210992 + -1.625 x = 2.154210992 + -1.625 Combine like terms: 2.154210992 + -1.625 = 0.529210992 x = 0.529210992 Simplifying x = 0.529210992Subproblem 2
x + 1.625 = -2.154210992 Simplifying x + 1.625 = -2.154210992 Reorder the terms: 1.625 + x = -2.154210992 Solving 1.625 + x = -2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -2.154210992 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -2.154210992 + -1.625 x = -2.154210992 + -1.625 Combine like terms: -2.154210992 + -1.625 = -3.779210992 x = -3.779210992 Simplifying x = -3.779210992Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.529210992, -3.779210992}
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