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Simplifying g2 + 5g + -56 = 0 Reorder the terms: -56 + 5g + g2 = 0 Solving -56 + 5g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 5g + 56 + g2 = 0 + 56 Reorder the terms: -56 + 56 + 5g + g2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 5g + g2 = 0 + 56 5g + g2 = 0 + 56 Combine like terms: 0 + 56 = 56 5g + g2 = 56 The g term is 5g. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5g + 6.25 + g2 = 56 + 6.25 Reorder the terms: 6.25 + 5g + g2 = 56 + 6.25 Combine like terms: 56 + 6.25 = 62.25 6.25 + 5g + g2 = 62.25 Factor a perfect square on the left side: (g + 2.5)(g + 2.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (g + 2.5) equal to 7.889866919 and -7.889866919.Subproblem 1
g + 2.5 = 7.889866919 Simplifying g + 2.5 = 7.889866919 Reorder the terms: 2.5 + g = 7.889866919 Solving 2.5 + g = 7.889866919 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + g = 7.889866919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + g = 7.889866919 + -2.5 g = 7.889866919 + -2.5 Combine like terms: 7.889866919 + -2.5 = 5.389866919 g = 5.389866919 Simplifying g = 5.389866919Subproblem 2
g + 2.5 = -7.889866919 Simplifying g + 2.5 = -7.889866919 Reorder the terms: 2.5 + g = -7.889866919 Solving 2.5 + g = -7.889866919 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + g = -7.889866919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + g = -7.889866919 + -2.5 g = -7.889866919 + -2.5 Combine like terms: -7.889866919 + -2.5 = -10.389866919 g = -10.389866919 Simplifying g = -10.389866919Solution
The solution to the problem is based on the solutions from the subproblems. g = {5.389866919, -10.389866919}
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