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Simplifying 5x2 + 4x + -37 = 0 Reorder the terms: -37 + 4x + 5x2 = 0 Solving -37 + 4x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.4 + 0.8x + x2 = 0 Move the constant term to the right: Add '7.4' to each side of the equation. -7.4 + 0.8x + 7.4 + x2 = 0 + 7.4 Reorder the terms: -7.4 + 7.4 + 0.8x + x2 = 0 + 7.4 Combine like terms: -7.4 + 7.4 = 0.0 0.0 + 0.8x + x2 = 0 + 7.4 0.8x + x2 = 0 + 7.4 Combine like terms: 0 + 7.4 = 7.4 0.8x + x2 = 7.4 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 7.4 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 7.4 + 0.16 Combine like terms: 7.4 + 0.16 = 7.56 0.16 + 0.8x + x2 = 7.56 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 7.56 Calculate the square root of the right side: 2.749545417 Break this problem into two subproblems by setting (x + 0.4) equal to 2.749545417 and -2.749545417.Subproblem 1
x + 0.4 = 2.749545417 Simplifying x + 0.4 = 2.749545417 Reorder the terms: 0.4 + x = 2.749545417 Solving 0.4 + x = 2.749545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.749545417 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.749545417 + -0.4 x = 2.749545417 + -0.4 Combine like terms: 2.749545417 + -0.4 = 2.349545417 x = 2.349545417 Simplifying x = 2.349545417Subproblem 2
x + 0.4 = -2.749545417 Simplifying x + 0.4 = -2.749545417 Reorder the terms: 0.4 + x = -2.749545417 Solving 0.4 + x = -2.749545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.749545417 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.749545417 + -0.4 x = -2.749545417 + -0.4 Combine like terms: -2.749545417 + -0.4 = -3.149545417 x = -3.149545417 Simplifying x = -3.149545417Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.349545417, -3.149545417}
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