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Simplifying 15x2 + 51x = 42 Reorder the terms: 51x + 15x2 = 42 Solving 51x + 15x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 51x + 15x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 51x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + 17x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-14 + 17x + 5x2)' equal to zero and attempt to solve: Simplifying -14 + 17x + 5x2 = 0 Solving -14 + 17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + 3.4x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 3.4x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 3.4x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 3.4x + x2 = 0 + 2.8 3.4x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 3.4x + x2 = 2.8 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = 2.8 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = 2.8 + 2.89 Combine like terms: 2.8 + 2.89 = 5.69 2.89 + 3.4x + x2 = 5.69 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 5.69 Calculate the square root of the right side: 2.385372088 Break this problem into two subproblems by setting (x + 1.7) equal to 2.385372088 and -2.385372088.Subproblem 1
x + 1.7 = 2.385372088 Simplifying x + 1.7 = 2.385372088 Reorder the terms: 1.7 + x = 2.385372088 Solving 1.7 + x = 2.385372088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 2.385372088 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 2.385372088 + -1.7 x = 2.385372088 + -1.7 Combine like terms: 2.385372088 + -1.7 = 0.685372088 x = 0.685372088 Simplifying x = 0.685372088Subproblem 2
x + 1.7 = -2.385372088 Simplifying x + 1.7 = -2.385372088 Reorder the terms: 1.7 + x = -2.385372088 Solving 1.7 + x = -2.385372088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -2.385372088 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -2.385372088 + -1.7 x = -2.385372088 + -1.7 Combine like terms: -2.385372088 + -1.7 = -4.085372088 x = -4.085372088 Simplifying x = -4.085372088Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.685372088, -4.085372088}Solution
x = {0.685372088, -4.085372088}
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