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Simplifying 2x(5x + 8) = 51 + 1 + -2 Reorder the terms: 2x(8 + 5x) = 51 + 1 + -2 (8 * 2x + 5x * 2x) = 51 + 1 + -2 (16x + 10x2) = 51 + 1 + -2 Combine like terms: 51 + 1 = 52 16x + 10x2 = 52 + -2 Combine like terms: 52 + -2 = 50 16x + 10x2 = 50 Solving 16x + 10x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 16x + 10x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 16x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 8x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 8x + 5x2)' equal to zero and attempt to solve: Simplifying -25 + 8x + 5x2 = 0 Solving -25 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + 1.6x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 1.6x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 1.6x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 1.6x + x2 = 0 + 5 1.6x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 1.6x + x2 = 5 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 = 5 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 5 + 0.64 Combine like terms: 5 + 0.64 = 5.64 0.64 + 1.6x + x2 = 5.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 5.64 Calculate the square root of the right side: 2.374868417 Break this problem into two subproblems by setting (x + 0.8) equal to 2.374868417 and -2.374868417.Subproblem 1
x + 0.8 = 2.374868417 Simplifying x + 0.8 = 2.374868417 Reorder the terms: 0.8 + x = 2.374868417 Solving 0.8 + x = 2.374868417 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 = 2.374868417 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 2.374868417 + -0.8 x = 2.374868417 + -0.8 Combine like terms: 2.374868417 + -0.8 = 1.574868417 x = 1.574868417 Simplifying x = 1.574868417Subproblem 2
x + 0.8 = -2.374868417 Simplifying x + 0.8 = -2.374868417 Reorder the terms: 0.8 + x = -2.374868417 Solving 0.8 + x = -2.374868417 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 = -2.374868417 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -2.374868417 + -0.8 x = -2.374868417 + -0.8 Combine like terms: -2.374868417 + -0.8 = -3.174868417 x = -3.174868417 Simplifying x = -3.174868417Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.574868417, -3.174868417}Solution
x = {1.574868417, -3.174868417}
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