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Simplifying 0 = -9x2 + -62x + -40 Reorder the terms: 0 = -40 + -62x + -9x2 Solving 0 = -40 + -62x + -9x2 Solving for variable 'x'. Combine like terms: 0 + 40 = 40 40 + 62x + 9x2 = -40 + -62x + -9x2 + 40 + 62x + 9x2 Reorder the terms: 40 + 62x + 9x2 = -40 + 40 + -62x + 62x + -9x2 + 9x2 Combine like terms: -40 + 40 = 0 40 + 62x + 9x2 = 0 + -62x + 62x + -9x2 + 9x2 40 + 62x + 9x2 = -62x + 62x + -9x2 + 9x2 Combine like terms: -62x + 62x = 0 40 + 62x + 9x2 = 0 + -9x2 + 9x2 40 + 62x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 40 + 62x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4.444444444 + 6.888888889x + x2 = 0 Move the constant term to the right: Add '-4.444444444' to each side of the equation. 4.444444444 + 6.888888889x + -4.444444444 + x2 = 0 + -4.444444444 Reorder the terms: 4.444444444 + -4.444444444 + 6.888888889x + x2 = 0 + -4.444444444 Combine like terms: 4.444444444 + -4.444444444 = 0.000000000 0.000000000 + 6.888888889x + x2 = 0 + -4.444444444 6.888888889x + x2 = 0 + -4.444444444 Combine like terms: 0 + -4.444444444 = -4.444444444 6.888888889x + x2 = -4.444444444 The x term is 6.888888889x. Take half its coefficient (3.444444445). Square it (11.86419753) and add it to both sides. Add '11.86419753' to each side of the equation. 6.888888889x + 11.86419753 + x2 = -4.444444444 + 11.86419753 Reorder the terms: 11.86419753 + 6.888888889x + x2 = -4.444444444 + 11.86419753 Combine like terms: -4.444444444 + 11.86419753 = 7.419753086 11.86419753 + 6.888888889x + x2 = 7.419753086 Factor a perfect square on the left side: (x + 3.444444445)(x + 3.444444445) = 7.419753086 Calculate the square root of the right side: 2.723922372 Break this problem into two subproblems by setting (x + 3.444444445) equal to 2.723922372 and -2.723922372.Subproblem 1
x + 3.444444445 = 2.723922372 Simplifying x + 3.444444445 = 2.723922372 Reorder the terms: 3.444444445 + x = 2.723922372 Solving 3.444444445 + x = 2.723922372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.444444445' to each side of the equation. 3.444444445 + -3.444444445 + x = 2.723922372 + -3.444444445 Combine like terms: 3.444444445 + -3.444444445 = 0.000000000 0.000000000 + x = 2.723922372 + -3.444444445 x = 2.723922372 + -3.444444445 Combine like terms: 2.723922372 + -3.444444445 = -0.720522073 x = -0.720522073 Simplifying x = -0.720522073Subproblem 2
x + 3.444444445 = -2.723922372 Simplifying x + 3.444444445 = -2.723922372 Reorder the terms: 3.444444445 + x = -2.723922372 Solving 3.444444445 + x = -2.723922372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.444444445' to each side of the equation. 3.444444445 + -3.444444445 + x = -2.723922372 + -3.444444445 Combine like terms: 3.444444445 + -3.444444445 = 0.000000000 0.000000000 + x = -2.723922372 + -3.444444445 x = -2.723922372 + -3.444444445 Combine like terms: -2.723922372 + -3.444444445 = -6.168366817 x = -6.168366817 Simplifying x = -6.168366817Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.720522073, -6.168366817}
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