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Simplifying 9x2 + -62x + -90 = 0 Reorder the terms: -90 + -62x + 9x2 = 0 Solving -90 + -62x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -10 + -6.888888889x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -6.888888889x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -6.888888889x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -6.888888889x + x2 = 0 + 10 -6.888888889x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -6.888888889x + x2 = 10 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 = 10 + 11.86419753 Reorder the terms: 11.86419753 + -6.888888889x + x2 = 10 + 11.86419753 Combine like terms: 10 + 11.86419753 = 21.86419753 11.86419753 + -6.888888889x + x2 = 21.86419753 Factor a perfect square on the left side: (x + -3.444444445)(x + -3.444444445) = 21.86419753 Calculate the square root of the right side: 4.675916758 Break this problem into two subproblems by setting (x + -3.444444445) equal to 4.675916758 and -4.675916758.Subproblem 1
x + -3.444444445 = 4.675916758 Simplifying x + -3.444444445 = 4.675916758 Reorder the terms: -3.444444445 + x = 4.675916758 Solving -3.444444445 + x = 4.675916758 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 = 4.675916758 + 3.444444445 Combine like terms: -3.444444445 + 3.444444445 = 0.000000000 0.000000000 + x = 4.675916758 + 3.444444445 x = 4.675916758 + 3.444444445 Combine like terms: 4.675916758 + 3.444444445 = 8.120361203 x = 8.120361203 Simplifying x = 8.120361203Subproblem 2
x + -3.444444445 = -4.675916758 Simplifying x + -3.444444445 = -4.675916758 Reorder the terms: -3.444444445 + x = -4.675916758 Solving -3.444444445 + x = -4.675916758 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 = -4.675916758 + 3.444444445 Combine like terms: -3.444444445 + 3.444444445 = 0.000000000 0.000000000 + x = -4.675916758 + 3.444444445 x = -4.675916758 + 3.444444445 Combine like terms: -4.675916758 + 3.444444445 = -1.231472313 x = -1.231472313 Simplifying x = -1.231472313Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.120361203, -1.231472313}
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