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Simplifying 3x2 + -40 = -6x2 + -5x + -24 Reorder the terms: -40 + 3x2 = -6x2 + -5x + -24 Reorder the terms: -40 + 3x2 = -24 + -5x + -6x2 Solving -40 + 3x2 = -24 + -5x + -6x2 Solving for variable 'x'. Reorder the terms: -40 + 24 + 5x + 3x2 + 6x2 = -24 + -5x + -6x2 + 24 + 5x + 6x2 Combine like terms: -40 + 24 = -16 -16 + 5x + 3x2 + 6x2 = -24 + -5x + -6x2 + 24 + 5x + 6x2 Combine like terms: 3x2 + 6x2 = 9x2 -16 + 5x + 9x2 = -24 + -5x + -6x2 + 24 + 5x + 6x2 Reorder the terms: -16 + 5x + 9x2 = -24 + 24 + -5x + 5x + -6x2 + 6x2 Combine like terms: -24 + 24 = 0 -16 + 5x + 9x2 = 0 + -5x + 5x + -6x2 + 6x2 -16 + 5x + 9x2 = -5x + 5x + -6x2 + 6x2 Combine like terms: -5x + 5x = 0 -16 + 5x + 9x2 = 0 + -6x2 + 6x2 -16 + 5x + 9x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -16 + 5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + 0.5555555556x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + 0.5555555556x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + 0.5555555556x + x2 = 0 + 1.777777778 0.5555555556x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 0.5555555556x + x2 = 1.777777778 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 1.777777778 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 1.777777778 + 0.07716049384 Combine like terms: 1.777777778 + 0.07716049384 = 1.85493827184 0.07716049384 + 0.5555555556x + x2 = 1.85493827184 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 1.85493827184 Calculate the square root of the right side: 1.361961186 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 1.361961186 and -1.361961186.Subproblem 1
x + 0.2777777778 = 1.361961186 Simplifying x + 0.2777777778 = 1.361961186 Reorder the terms: 0.2777777778 + x = 1.361961186 Solving 0.2777777778 + x = 1.361961186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 1.361961186 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 1.361961186 + -0.2777777778 x = 1.361961186 + -0.2777777778 Combine like terms: 1.361961186 + -0.2777777778 = 1.0841834082 x = 1.0841834082 Simplifying x = 1.0841834082Subproblem 2
x + 0.2777777778 = -1.361961186 Simplifying x + 0.2777777778 = -1.361961186 Reorder the terms: 0.2777777778 + x = -1.361961186 Solving 0.2777777778 + x = -1.361961186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -1.361961186 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -1.361961186 + -0.2777777778 x = -1.361961186 + -0.2777777778 Combine like terms: -1.361961186 + -0.2777777778 = -1.6397389638 x = -1.6397389638 Simplifying x = -1.6397389638Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0841834082, -1.6397389638}
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