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Simplifying 10x(2x + 5) = 19 Reorder the terms: 10x(5 + 2x) = 19 (5 * 10x + 2x * 10x) = 19 (50x + 20x2) = 19 Solving 50x + 20x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 50x + 20x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 50x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.95 + 2.5x + x2 = 0.0 Move the constant term to the right: Add '0.95' to each side of the equation. -0.95 + 2.5x + 0.95 + x2 = 0.0 + 0.95 Reorder the terms: -0.95 + 0.95 + 2.5x + x2 = 0.0 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + 2.5x + x2 = 0.0 + 0.95 2.5x + x2 = 0.0 + 0.95 Combine like terms: 0.0 + 0.95 = 0.95 2.5x + x2 = 0.95 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 0.95 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.95 + 1.5625 Combine like terms: 0.95 + 1.5625 = 2.5125 1.5625 + 2.5x + x2 = 2.5125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.5125 Calculate the square root of the right side: 1.585086748 Break this problem into two subproblems by setting (x + 1.25) equal to 1.585086748 and -1.585086748.Subproblem 1
x + 1.25 = 1.585086748 Simplifying x + 1.25 = 1.585086748 Reorder the terms: 1.25 + x = 1.585086748 Solving 1.25 + x = 1.585086748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.585086748 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.585086748 + -1.25 x = 1.585086748 + -1.25 Combine like terms: 1.585086748 + -1.25 = 0.335086748 x = 0.335086748 Simplifying x = 0.335086748Subproblem 2
x + 1.25 = -1.585086748 Simplifying x + 1.25 = -1.585086748 Reorder the terms: 1.25 + x = -1.585086748 Solving 1.25 + x = -1.585086748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.585086748 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.585086748 + -1.25 x = -1.585086748 + -1.25 Combine like terms: -1.585086748 + -1.25 = -2.835086748 x = -2.835086748 Simplifying x = -2.835086748Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.335086748, -2.835086748}
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