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Simplifying 5x(5x + 8) = 49 Reorder the terms: 5x(8 + 5x) = 49 (8 * 5x + 5x * 5x) = 49 (40x + 25x2) = 49 Solving 40x + 25x2 = 49 Solving for variable 'x'. Reorder the terms: -49 + 40x + 25x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 40x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.96 + 1.6x + x2 = 0 Move the constant term to the right: Add '1.96' to each side of the equation. -1.96 + 1.6x + 1.96 + x2 = 0 + 1.96 Reorder the terms: -1.96 + 1.96 + 1.6x + x2 = 0 + 1.96 Combine like terms: -1.96 + 1.96 = 0.00 0.00 + 1.6x + x2 = 0 + 1.96 1.6x + x2 = 0 + 1.96 Combine like terms: 0 + 1.96 = 1.96 1.6x + x2 = 1.96 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 1.96 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 1.96 + 0.64 Combine like terms: 1.96 + 0.64 = 2.6 0.64 + 1.6x + x2 = 2.6 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 2.6 Calculate the square root of the right side: 1.61245155 Break this problem into two subproblems by setting (x + 0.8) equal to 1.61245155 and -1.61245155.Subproblem 1
x + 0.8 = 1.61245155 Simplifying x + 0.8 = 1.61245155 Reorder the terms: 0.8 + x = 1.61245155 Solving 0.8 + x = 1.61245155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.61245155 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.61245155 + -0.8 x = 1.61245155 + -0.8 Combine like terms: 1.61245155 + -0.8 = 0.81245155 x = 0.81245155 Simplifying x = 0.81245155Subproblem 2
x + 0.8 = -1.61245155 Simplifying x + 0.8 = -1.61245155 Reorder the terms: 0.8 + x = -1.61245155 Solving 0.8 + x = -1.61245155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.61245155 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.61245155 + -0.8 x = -1.61245155 + -0.8 Combine like terms: -1.61245155 + -0.8 = -2.41245155 x = -2.41245155 Simplifying x = -2.41245155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.81245155, -2.41245155}
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