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Simplifying 5x2 + 10x = 36x + 36 Reorder the terms: 10x + 5x2 = 36x + 36 Reorder the terms: 10x + 5x2 = 36 + 36x Solving 10x + 5x2 = 36 + 36x Solving for variable 'x'. Reorder the terms: -36 + 10x + -36x + 5x2 = 36 + 36x + -36 + -36x Combine like terms: 10x + -36x = -26x -36 + -26x + 5x2 = 36 + 36x + -36 + -36x Reorder the terms: -36 + -26x + 5x2 = 36 + -36 + 36x + -36x Combine like terms: 36 + -36 = 0 -36 + -26x + 5x2 = 0 + 36x + -36x -36 + -26x + 5x2 = 36x + -36x Combine like terms: 36x + -36x = 0 -36 + -26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + -5.2x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + -5.2x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + -5.2x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -5.2x + x2 = 0 + 7.2 -5.2x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 -5.2x + x2 = 7.2 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 = 7.2 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = 7.2 + 6.76 Combine like terms: 7.2 + 6.76 = 13.96 6.76 + -5.2x + x2 = 13.96 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 13.96 Calculate the square root of the right side: 3.736308338 Break this problem into two subproblems by setting (x + -2.6) equal to 3.736308338 and -3.736308338.Subproblem 1
x + -2.6 = 3.736308338 Simplifying x + -2.6 = 3.736308338 Reorder the terms: -2.6 + x = 3.736308338 Solving -2.6 + x = 3.736308338 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 = 3.736308338 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 3.736308338 + 2.6 x = 3.736308338 + 2.6 Combine like terms: 3.736308338 + 2.6 = 6.336308338 x = 6.336308338 Simplifying x = 6.336308338Subproblem 2
x + -2.6 = -3.736308338 Simplifying x + -2.6 = -3.736308338 Reorder the terms: -2.6 + x = -3.736308338 Solving -2.6 + x = -3.736308338 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 = -3.736308338 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -3.736308338 + 2.6 x = -3.736308338 + 2.6 Combine like terms: -3.736308338 + 2.6 = -1.136308338 x = -1.136308338 Simplifying x = -1.136308338Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.336308338, -1.136308338}
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