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Simplifying 5x2 + x = 37 Reorder the terms: x + 5x2 = 37 Solving x + 5x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + x + 5x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.4 + 0.2x + x2 = 0 Move the constant term to the right: Add '7.4' to each side of the equation. -7.4 + 0.2x + 7.4 + x2 = 0 + 7.4 Reorder the terms: -7.4 + 7.4 + 0.2x + x2 = 0 + 7.4 Combine like terms: -7.4 + 7.4 = 0.0 0.0 + 0.2x + x2 = 0 + 7.4 0.2x + x2 = 0 + 7.4 Combine like terms: 0 + 7.4 = 7.4 0.2x + x2 = 7.4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2x + 0.25 + x2 = 7.4 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = 7.4 + 0.25 Combine like terms: 7.4 + 0.25 = 7.65 0.25 + 0.2x + x2 = 7.65 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.65 Calculate the square root of the right side: 2.765863337 Break this problem into two subproblems by setting (x + 0.5) equal to 2.765863337 and -2.765863337.Subproblem 1
x + 0.5 = 2.765863337 Simplifying x + 0.5 = 2.765863337 Reorder the terms: 0.5 + x = 2.765863337 Solving 0.5 + x = 2.765863337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.765863337 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.765863337 + -0.5 x = 2.765863337 + -0.5 Combine like terms: 2.765863337 + -0.5 = 2.265863337 x = 2.265863337 Simplifying x = 2.265863337Subproblem 2
x + 0.5 = -2.765863337 Simplifying x + 0.5 = -2.765863337 Reorder the terms: 0.5 + x = -2.765863337 Solving 0.5 + x = -2.765863337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.765863337 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.765863337 + -0.5 x = -2.765863337 + -0.5 Combine like terms: -2.765863337 + -0.5 = -3.265863337 x = -3.265863337 Simplifying x = -3.265863337Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.265863337, -3.265863337}
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