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Simplifying g2 + -0.7g = 7 Reorder the terms: -0.7g + g2 = 7 Solving -0.7g + g2 = 7 Solving for variable 'g'. Reorder the terms: -7 + -0.7g + g2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -0.7g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.7g + 7 + g2 = 0 + 7 Reorder the terms: -7 + 7 + -0.7g + g2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.7g + g2 = 0 + 7 -0.7g + g2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.7g + g2 = 7 The g term is -0.7g. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7g + 0.1225 + g2 = 7 + 0.1225 Reorder the terms: 0.1225 + -0.7g + g2 = 7 + 0.1225 Combine like terms: 7 + 0.1225 = 7.1225 0.1225 + -0.7g + g2 = 7.1225 Factor a perfect square on the left side: (g + -0.35)(g + -0.35) = 7.1225 Calculate the square root of the right side: 2.668801229 Break this problem into two subproblems by setting (g + -0.35) equal to 2.668801229 and -2.668801229.Subproblem 1
g + -0.35 = 2.668801229 Simplifying g + -0.35 = 2.668801229 Reorder the terms: -0.35 + g = 2.668801229 Solving -0.35 + g = 2.668801229 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + g = 2.668801229 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + g = 2.668801229 + 0.35 g = 2.668801229 + 0.35 Combine like terms: 2.668801229 + 0.35 = 3.018801229 g = 3.018801229 Simplifying g = 3.018801229Subproblem 2
g + -0.35 = -2.668801229 Simplifying g + -0.35 = -2.668801229 Reorder the terms: -0.35 + g = -2.668801229 Solving -0.35 + g = -2.668801229 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + g = -2.668801229 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + g = -2.668801229 + 0.35 g = -2.668801229 + 0.35 Combine like terms: -2.668801229 + 0.35 = -2.318801229 g = -2.318801229 Simplifying g = -2.318801229Solution
The solution to the problem is based on the solutions from the subproblems. g = {3.018801229, -2.318801229}
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