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Simplifying -446 = 7g(g + -834) + -663 Reorder the terms: -446 = 7g(-834 + g) + -663 -446 = (-834 * 7g + g * 7g) + -663 -446 = (-5838g + 7g2) + -663 Reorder the terms: -446 = -663 + -5838g + 7g2 Solving -446 = -663 + -5838g + 7g2 Solving for variable 'g'. Combine like terms: -446 + 663 = 217 217 + 5838g + -7g2 = -663 + -5838g + 7g2 + 663 + 5838g + -7g2 Reorder the terms: 217 + 5838g + -7g2 = -663 + 663 + -5838g + 5838g + 7g2 + -7g2 Combine like terms: -663 + 663 = 0 217 + 5838g + -7g2 = 0 + -5838g + 5838g + 7g2 + -7g2 217 + 5838g + -7g2 = -5838g + 5838g + 7g2 + -7g2 Combine like terms: -5838g + 5838g = 0 217 + 5838g + -7g2 = 0 + 7g2 + -7g2 217 + 5838g + -7g2 = 7g2 + -7g2 Combine like terms: 7g2 + -7g2 = 0 217 + 5838g + -7g2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(31 + 834g + -1g2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(31 + 834g + -1g2)' equal to zero and attempt to solve: Simplifying 31 + 834g + -1g2 = 0 Solving 31 + 834g + -1g2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + -834g + g2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + -834g + 31 + g2 = 0 + 31 Reorder the terms: -31 + 31 + -834g + g2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -834g + g2 = 0 + 31 -834g + g2 = 0 + 31 Combine like terms: 0 + 31 = 31 -834g + g2 = 31 The g term is -834g. Take half its coefficient (-417). Square it (173889) and add it to both sides. Add '173889' to each side of the equation. -834g + 173889 + g2 = 31 + 173889 Reorder the terms: 173889 + -834g + g2 = 31 + 173889 Combine like terms: 31 + 173889 = 173920 173889 + -834g + g2 = 173920 Factor a perfect square on the left side: (g + -417)(g + -417) = 173920 Calculate the square root of the right side: 417.037168607 Break this problem into two subproblems by setting (g + -417) equal to 417.037168607 and -417.037168607.Subproblem 1
g + -417 = 417.037168607 Simplifying g + -417 = 417.037168607 Reorder the terms: -417 + g = 417.037168607 Solving -417 + g = 417.037168607 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '417' to each side of the equation. -417 + 417 + g = 417.037168607 + 417 Combine like terms: -417 + 417 = 0 0 + g = 417.037168607 + 417 g = 417.037168607 + 417 Combine like terms: 417.037168607 + 417 = 834.037168607 g = 834.037168607 Simplifying g = 834.037168607Subproblem 2
g + -417 = -417.037168607 Simplifying g + -417 = -417.037168607 Reorder the terms: -417 + g = -417.037168607 Solving -417 + g = -417.037168607 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '417' to each side of the equation. -417 + 417 + g = -417.037168607 + 417 Combine like terms: -417 + 417 = 0 0 + g = -417.037168607 + 417 g = -417.037168607 + 417 Combine like terms: -417.037168607 + 417 = -0.037168607 g = -0.037168607 Simplifying g = -0.037168607Solution
The solution to the problem is based on the solutions from the subproblems. g = {834.037168607, -0.037168607}Solution
g = {834.037168607, -0.037168607}
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