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Simplifying 5x(x + 2) = 126 Reorder the terms: 5x(2 + x) = 126 (2 * 5x + x * 5x) = 126 (10x + 5x2) = 126 Solving 10x + 5x2 = 126 Solving for variable 'x'. Reorder the terms: -126 + 10x + 5x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -25.2 + 2x + x2 = 0 Move the constant term to the right: Add '25.2' to each side of the equation. -25.2 + 2x + 25.2 + x2 = 0 + 25.2 Reorder the terms: -25.2 + 25.2 + 2x + x2 = 0 + 25.2 Combine like terms: -25.2 + 25.2 = 0.0 0.0 + 2x + x2 = 0 + 25.2 2x + x2 = 0 + 25.2 Combine like terms: 0 + 25.2 = 25.2 2x + x2 = 25.2 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 25.2 + 1 Reorder the terms: 1 + 2x + x2 = 25.2 + 1 Combine like terms: 25.2 + 1 = 26.2 1 + 2x + x2 = 26.2 Factor a perfect square on the left side: (x + 1)(x + 1) = 26.2 Calculate the square root of the right side: 5.118593557 Break this problem into two subproblems by setting (x + 1) equal to 5.118593557 and -5.118593557.Subproblem 1
x + 1 = 5.118593557 Simplifying x + 1 = 5.118593557 Reorder the terms: 1 + x = 5.118593557 Solving 1 + x = 5.118593557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.118593557 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.118593557 + -1 x = 5.118593557 + -1 Combine like terms: 5.118593557 + -1 = 4.118593557 x = 4.118593557 Simplifying x = 4.118593557Subproblem 2
x + 1 = -5.118593557 Simplifying x + 1 = -5.118593557 Reorder the terms: 1 + x = -5.118593557 Solving 1 + x = -5.118593557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.118593557 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.118593557 + -1 x = -5.118593557 + -1 Combine like terms: -5.118593557 + -1 = -6.118593557 x = -6.118593557 Simplifying x = -6.118593557Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.118593557, -6.118593557}
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