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Simplifying 5x2 + 2x = 63 Reorder the terms: 2x + 5x2 = 63 Solving 2x + 5x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + 2x + 5x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.6 + 0.4x + x2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + 0.4x + 12.6 + x2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + 0.4x + x2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + 0.4x + x2 = 0 + 12.6 0.4x + x2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 0.4x + x2 = 12.6 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 12.6 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 12.6 + 0.04 Combine like terms: 12.6 + 0.04 = 12.64 0.04 + 0.4x + x2 = 12.64 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 12.64 Calculate the square root of the right side: 3.555277767 Break this problem into two subproblems by setting (x + 0.2) equal to 3.555277767 and -3.555277767.Subproblem 1
x + 0.2 = 3.555277767 Simplifying x + 0.2 = 3.555277767 Reorder the terms: 0.2 + x = 3.555277767 Solving 0.2 + x = 3.555277767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 3.555277767 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 3.555277767 + -0.2 x = 3.555277767 + -0.2 Combine like terms: 3.555277767 + -0.2 = 3.355277767 x = 3.355277767 Simplifying x = 3.355277767Subproblem 2
x + 0.2 = -3.555277767 Simplifying x + 0.2 = -3.555277767 Reorder the terms: 0.2 + x = -3.555277767 Solving 0.2 + x = -3.555277767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -3.555277767 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -3.555277767 + -0.2 x = -3.555277767 + -0.2 Combine like terms: -3.555277767 + -0.2 = -3.755277767 x = -3.755277767 Simplifying x = -3.755277767Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.355277767, -3.755277767}
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