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Simplifying 0.50(x) + 13 = 14(x) * 1.25(x) Reorder the terms: 13 + 0.50x = 14(x) * 1.25(x) Reorder the terms for easier multiplication: 13 + 0.50x = 14 * 1.25x * x Multiply 14 * 1.25 13 + 0.50x = 17.5x * x Multiply x * x 13 + 0.50x = 17.5x2 Solving 13 + 0.50x = 17.5x2 Solving for variable 'x'. Combine like terms: 17.5x2 + -17.5x2 = 0.0 13 + 0.50x + -17.5x2 = 0.0 Begin completing the square. Divide all terms by -17.5 the coefficient of the squared term: Divide each side by '-17.5'. -0.7428571429 + -0.02857142857x + x2 = 0 Move the constant term to the right: Add '0.7428571429' to each side of the equation. -0.7428571429 + -0.02857142857x + 0.7428571429 + x2 = 0 + 0.7428571429 Reorder the terms: -0.7428571429 + 0.7428571429 + -0.02857142857x + x2 = 0 + 0.7428571429 Combine like terms: -0.7428571429 + 0.7428571429 = 0.0000000000 0.0000000000 + -0.02857142857x + x2 = 0 + 0.7428571429 -0.02857142857x + x2 = 0 + 0.7428571429 Combine like terms: 0 + 0.7428571429 = 0.7428571429 -0.02857142857x + x2 = 0.7428571429 The x term is -0.02857142857x. Take half its coefficient (-0.01428571429). Square it (0.0002040816328) and add it to both sides. Add '0.0002040816328' to each side of the equation. -0.02857142857x + 0.0002040816328 + x2 = 0.7428571429 + 0.0002040816328 Reorder the terms: 0.0002040816328 + -0.02857142857x + x2 = 0.7428571429 + 0.0002040816328 Combine like terms: 0.7428571429 + 0.0002040816328 = 0.7430612245328 0.0002040816328 + -0.02857142857x + x2 = 0.7430612245328 Factor a perfect square on the left side: (x + -0.01428571429)(x + -0.01428571429) = 0.7430612245328 Calculate the square root of the right side: 0.862009991 Break this problem into two subproblems by setting (x + -0.01428571429) equal to 0.862009991 and -0.862009991.Subproblem 1
x + -0.01428571429 = 0.862009991 Simplifying x + -0.01428571429 = 0.862009991 Reorder the terms: -0.01428571429 + x = 0.862009991 Solving -0.01428571429 + x = 0.862009991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01428571429' to each side of the equation. -0.01428571429 + 0.01428571429 + x = 0.862009991 + 0.01428571429 Combine like terms: -0.01428571429 + 0.01428571429 = 0.00000000000 0.00000000000 + x = 0.862009991 + 0.01428571429 x = 0.862009991 + 0.01428571429 Combine like terms: 0.862009991 + 0.01428571429 = 0.87629570529 x = 0.87629570529 Simplifying x = 0.87629570529Subproblem 2
x + -0.01428571429 = -0.862009991 Simplifying x + -0.01428571429 = -0.862009991 Reorder the terms: -0.01428571429 + x = -0.862009991 Solving -0.01428571429 + x = -0.862009991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01428571429' to each side of the equation. -0.01428571429 + 0.01428571429 + x = -0.862009991 + 0.01428571429 Combine like terms: -0.01428571429 + 0.01428571429 = 0.00000000000 0.00000000000 + x = -0.862009991 + 0.01428571429 x = -0.862009991 + 0.01428571429 Combine like terms: -0.862009991 + 0.01428571429 = -0.84772427671 x = -0.84772427671 Simplifying x = -0.84772427671Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.87629570529, -0.84772427671}
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