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Simplifying 45x2 + 28x = 630 Reorder the terms: 28x + 45x2 = 630 Solving 28x + 45x2 = 630 Solving for variable 'x'. Reorder the terms: -630 + 28x + 45x2 = 630 + -630 Combine like terms: 630 + -630 = 0 -630 + 28x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -14 + 0.6222222222x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 0.6222222222x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 0.6222222222x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 0.6222222222x + x2 = 0 + 14 0.6222222222x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 0.6222222222x + x2 = 14 The x term is 0.6222222222x. Take half its coefficient (0.3111111111). Square it (0.09679012345) and add it to both sides. Add '0.09679012345' to each side of the equation. 0.6222222222x + 0.09679012345 + x2 = 14 + 0.09679012345 Reorder the terms: 0.09679012345 + 0.6222222222x + x2 = 14 + 0.09679012345 Combine like terms: 14 + 0.09679012345 = 14.09679012345 0.09679012345 + 0.6222222222x + x2 = 14.09679012345 Factor a perfect square on the left side: (x + 0.3111111111)(x + 0.3111111111) = 14.09679012345 Calculate the square root of the right side: 3.754569233 Break this problem into two subproblems by setting (x + 0.3111111111) equal to 3.754569233 and -3.754569233.Subproblem 1
x + 0.3111111111 = 3.754569233 Simplifying x + 0.3111111111 = 3.754569233 Reorder the terms: 0.3111111111 + x = 3.754569233 Solving 0.3111111111 + x = 3.754569233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3111111111' to each side of the equation. 0.3111111111 + -0.3111111111 + x = 3.754569233 + -0.3111111111 Combine like terms: 0.3111111111 + -0.3111111111 = 0.0000000000 0.0000000000 + x = 3.754569233 + -0.3111111111 x = 3.754569233 + -0.3111111111 Combine like terms: 3.754569233 + -0.3111111111 = 3.4434581219 x = 3.4434581219 Simplifying x = 3.4434581219Subproblem 2
x + 0.3111111111 = -3.754569233 Simplifying x + 0.3111111111 = -3.754569233 Reorder the terms: 0.3111111111 + x = -3.754569233 Solving 0.3111111111 + x = -3.754569233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3111111111' to each side of the equation. 0.3111111111 + -0.3111111111 + x = -3.754569233 + -0.3111111111 Combine like terms: 0.3111111111 + -0.3111111111 = 0.0000000000 0.0000000000 + x = -3.754569233 + -0.3111111111 x = -3.754569233 + -0.3111111111 Combine like terms: -3.754569233 + -0.3111111111 = -4.0656803441 x = -4.0656803441 Simplifying x = -4.0656803441Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4434581219, -4.0656803441}
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