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Simplifying 0.10x + 0.25x(x + 10) + 0.05(4)(x + 10) = 6.15 Reorder the terms: 0.10x + 0.25x(10 + x) + 0.05(4)(x + 10) = 6.15 0.10x + (10 * 0.25x + x * 0.25x) + 0.05(4)(x + 10) = 6.15 0.10x + (2.5x + 0.25x2) + 0.05(4)(x + 10) = 6.15 Reorder the terms: 0.10x + 2.5x + 0.25x2 + 0.05 * 4(10 + x) = 6.15 Multiply 0.05 * 4 0.10x + 2.5x + 0.25x2 + 0.2(10 + x) = 6.15 0.10x + 2.5x + 0.25x2 + (10 * 0.2 + x * 0.2) = 6.15 0.10x + 2.5x + 0.25x2 + (2 + 0.2x) = 6.15 Reorder the terms: 2 + 0.10x + 2.5x + 0.2x + 0.25x2 = 6.15 Combine like terms: 0.10x + 2.5x = 2.6x 2 + 2.6x + 0.2x + 0.25x2 = 6.15 Combine like terms: 2.6x + 0.2x = 2.8x 2 + 2.8x + 0.25x2 = 6.15 Solving 2 + 2.8x + 0.25x2 = 6.15 Solving for variable 'x'. Reorder the terms: 2 + -6.15 + 2.8x + 0.25x2 = 6.15 + -6.15 Combine like terms: 2 + -6.15 = -4.15 -4.15 + 2.8x + 0.25x2 = 6.15 + -6.15 Combine like terms: 6.15 + -6.15 = 0.00 -4.15 + 2.8x + 0.25x2 = 0.00 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -16.6 + 11.2x + x2 = 0 Move the constant term to the right: Add '16.6' to each side of the equation. -16.6 + 11.2x + 16.6 + x2 = 0 + 16.6 Reorder the terms: -16.6 + 16.6 + 11.2x + x2 = 0 + 16.6 Combine like terms: -16.6 + 16.6 = 0.0 0.0 + 11.2x + x2 = 0 + 16.6 11.2x + x2 = 0 + 16.6 Combine like terms: 0 + 16.6 = 16.6 11.2x + x2 = 16.6 The x term is 11.2x. Take half its coefficient (5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. 11.2x + 31.36 + x2 = 16.6 + 31.36 Reorder the terms: 31.36 + 11.2x + x2 = 16.6 + 31.36 Combine like terms: 16.6 + 31.36 = 47.96 31.36 + 11.2x + x2 = 47.96 Factor a perfect square on the left side: (x + 5.6)(x + 5.6) = 47.96 Calculate the square root of the right side: 6.925315877 Break this problem into two subproblems by setting (x + 5.6) equal to 6.925315877 and -6.925315877.Subproblem 1
x + 5.6 = 6.925315877 Simplifying x + 5.6 = 6.925315877 Reorder the terms: 5.6 + x = 6.925315877 Solving 5.6 + x = 6.925315877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = 6.925315877 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = 6.925315877 + -5.6 x = 6.925315877 + -5.6 Combine like terms: 6.925315877 + -5.6 = 1.325315877 x = 1.325315877 Simplifying x = 1.325315877Subproblem 2
x + 5.6 = -6.925315877 Simplifying x + 5.6 = -6.925315877 Reorder the terms: 5.6 + x = -6.925315877 Solving 5.6 + x = -6.925315877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = -6.925315877 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = -6.925315877 + -5.6 x = -6.925315877 + -5.6 Combine like terms: -6.925315877 + -5.6 = -12.525315877 x = -12.525315877 Simplifying x = -12.525315877Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.325315877, -12.525315877}
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