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Simplifying 5x2 = 6x + 10 Reorder the terms: 5x2 = 10 + 6x Solving 5x2 = 10 + 6x Solving for variable 'x'. Reorder the terms: -10 + -6x + 5x2 = 10 + 6x + -10 + -6x Reorder the terms: -10 + -6x + 5x2 = 10 + -10 + 6x + -6x Combine like terms: 10 + -10 = 0 -10 + -6x + 5x2 = 0 + 6x + -6x -10 + -6x + 5x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -10 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -1.2x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.2x + x2 = 0 + 2 -1.2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.2x + x2 = 2 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 2 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 2 + 0.36 Combine like terms: 2 + 0.36 = 2.36 0.36 + -1.2x + x2 = 2.36 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 2.36 Calculate the square root of the right side: 1.53622915 Break this problem into two subproblems by setting (x + -0.6) equal to 1.53622915 and -1.53622915.Subproblem 1
x + -0.6 = 1.53622915 Simplifying x + -0.6 = 1.53622915 Reorder the terms: -0.6 + x = 1.53622915 Solving -0.6 + x = 1.53622915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.53622915 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.53622915 + 0.6 x = 1.53622915 + 0.6 Combine like terms: 1.53622915 + 0.6 = 2.13622915 x = 2.13622915 Simplifying x = 2.13622915Subproblem 2
x + -0.6 = -1.53622915 Simplifying x + -0.6 = -1.53622915 Reorder the terms: -0.6 + x = -1.53622915 Solving -0.6 + x = -1.53622915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.53622915 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.53622915 + 0.6 x = -1.53622915 + 0.6 Combine like terms: -1.53622915 + 0.6 = -0.93622915 x = -0.93622915 Simplifying x = -0.93622915Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.13622915, -0.93622915}
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