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Simplifying 2x2 + 5(3 + -7 + 9x) + -6 = 16 Combine like terms: 3 + -7 = -4 2x2 + 5(-4 + 9x) + -6 = 16 2x2 + (-4 * 5 + 9x * 5) + -6 = 16 2x2 + (-20 + 45x) + -6 = 16 Reorder the terms: -20 + -6 + 45x + 2x2 = 16 Combine like terms: -20 + -6 = -26 -26 + 45x + 2x2 = 16 Solving -26 + 45x + 2x2 = 16 Solving for variable 'x'. Reorder the terms: -26 + -16 + 45x + 2x2 = 16 + -16 Combine like terms: -26 + -16 = -42 -42 + 45x + 2x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -42 + 45x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + 22.5x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 22.5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 22.5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 22.5x + x2 = 0 + 21 22.5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 22.5x + x2 = 21 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = 21 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 21 + 126.5625 Combine like terms: 21 + 126.5625 = 147.5625 126.5625 + 22.5x + x2 = 147.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 147.5625 Calculate the square root of the right side: 12.147530613 Break this problem into two subproblems by setting (x + 11.25) equal to 12.147530613 and -12.147530613.Subproblem 1
x + 11.25 = 12.147530613 Simplifying x + 11.25 = 12.147530613 Reorder the terms: 11.25 + x = 12.147530613 Solving 11.25 + x = 12.147530613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 12.147530613 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 12.147530613 + -11.25 x = 12.147530613 + -11.25 Combine like terms: 12.147530613 + -11.25 = 0.897530613 x = 0.897530613 Simplifying x = 0.897530613Subproblem 2
x + 11.25 = -12.147530613 Simplifying x + 11.25 = -12.147530613 Reorder the terms: 11.25 + x = -12.147530613 Solving 11.25 + x = -12.147530613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -12.147530613 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -12.147530613 + -11.25 x = -12.147530613 + -11.25 Combine like terms: -12.147530613 + -11.25 = -23.397530613 x = -23.397530613 Simplifying x = -23.397530613Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.897530613, -23.397530613}
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