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Simplifying 0.625x2 + 8x = 300 Reorder the terms: 8x + 0.625x2 = 300 Solving 8x + 0.625x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 8x + 0.625x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 8x + 0.625x2 = 0 Begin completing the square. Divide all terms by 0.625 the coefficient of the squared term: Divide each side by '0.625'. -480 + 12.8x + x2 = 0 Move the constant term to the right: Add '480' to each side of the equation. -480 + 12.8x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 12.8x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 12.8x + x2 = 0 + 480 12.8x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 12.8x + x2 = 480 The x term is 12.8x. Take half its coefficient (6.4). Square it (40.96) and add it to both sides. Add '40.96' to each side of the equation. 12.8x + 40.96 + x2 = 480 + 40.96 Reorder the terms: 40.96 + 12.8x + x2 = 480 + 40.96 Combine like terms: 480 + 40.96 = 520.96 40.96 + 12.8x + x2 = 520.96 Factor a perfect square on the left side: (x + 6.4)(x + 6.4) = 520.96 Calculate the square root of the right side: 22.824548188 Break this problem into two subproblems by setting (x + 6.4) equal to 22.824548188 and -22.824548188.Subproblem 1
x + 6.4 = 22.824548188 Simplifying x + 6.4 = 22.824548188 Reorder the terms: 6.4 + x = 22.824548188 Solving 6.4 + x = 22.824548188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.4' to each side of the equation. 6.4 + -6.4 + x = 22.824548188 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + x = 22.824548188 + -6.4 x = 22.824548188 + -6.4 Combine like terms: 22.824548188 + -6.4 = 16.424548188 x = 16.424548188 Simplifying x = 16.424548188Subproblem 2
x + 6.4 = -22.824548188 Simplifying x + 6.4 = -22.824548188 Reorder the terms: 6.4 + x = -22.824548188 Solving 6.4 + x = -22.824548188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.4' to each side of the equation. 6.4 + -6.4 + x = -22.824548188 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + x = -22.824548188 + -6.4 x = -22.824548188 + -6.4 Combine like terms: -22.824548188 + -6.4 = -29.224548188 x = -29.224548188 Simplifying x = -29.224548188Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.424548188, -29.224548188}
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