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Simplifying 2.5(x + 4) * 5x + 3 * 5x = 53.5 Reorder the terms: 2.5(4 + x) * 5x + 3 * 5x = 53.5 Reorder the terms for easier multiplication: 2.5 * 5x(4 + x) + 3 * 5x = 53.5 Multiply 2.5 * 5 12.5x(4 + x) + 3 * 5x = 53.5 (4 * 12.5x + x * 12.5x) + 3 * 5x = 53.5 (50x + 12.5x2) + 3 * 5x = 53.5 Multiply 3 * 5 50x + 12.5x2 + 15x = 53.5 Reorder the terms: 50x + 15x + 12.5x2 = 53.5 Combine like terms: 50x + 15x = 65x 65x + 12.5x2 = 53.5 Solving 65x + 12.5x2 = 53.5 Solving for variable 'x'. Reorder the terms: -53.5 + 65x + 12.5x2 = 53.5 + -53.5 Combine like terms: 53.5 + -53.5 = 0.0 -53.5 + 65x + 12.5x2 = 0.0 Begin completing the square. Divide all terms by 12.5 the coefficient of the squared term: Divide each side by '12.5'. -4.28 + 5.2x + x2 = 0 Move the constant term to the right: Add '4.28' to each side of the equation. -4.28 + 5.2x + 4.28 + x2 = 0 + 4.28 Reorder the terms: -4.28 + 4.28 + 5.2x + x2 = 0 + 4.28 Combine like terms: -4.28 + 4.28 = 0.00 0.00 + 5.2x + x2 = 0 + 4.28 5.2x + x2 = 0 + 4.28 Combine like terms: 0 + 4.28 = 4.28 5.2x + x2 = 4.28 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = 4.28 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 4.28 + 6.76 Combine like terms: 4.28 + 6.76 = 11.04 6.76 + 5.2x + x2 = 11.04 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 11.04 Calculate the square root of the right side: 3.322649545 Break this problem into two subproblems by setting (x + 2.6) equal to 3.322649545 and -3.322649545.Subproblem 1
x + 2.6 = 3.322649545 Simplifying x + 2.6 = 3.322649545 Reorder the terms: 2.6 + x = 3.322649545 Solving 2.6 + x = 3.322649545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 3.322649545 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 3.322649545 + -2.6 x = 3.322649545 + -2.6 Combine like terms: 3.322649545 + -2.6 = 0.722649545 x = 0.722649545 Simplifying x = 0.722649545Subproblem 2
x + 2.6 = -3.322649545 Simplifying x + 2.6 = -3.322649545 Reorder the terms: 2.6 + x = -3.322649545 Solving 2.6 + x = -3.322649545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -3.322649545 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -3.322649545 + -2.6 x = -3.322649545 + -2.6 Combine like terms: -3.322649545 + -2.6 = -5.922649545 x = -5.922649545 Simplifying x = -5.922649545Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.722649545, -5.922649545}
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