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Simplifying 8x2 + -15x + 4 + -5x + -9x2 = 0 Reorder the terms: 4 + -15x + -5x + 8x2 + -9x2 = 0 Combine like terms: -15x + -5x = -20x 4 + -20x + 8x2 + -9x2 = 0 Combine like terms: 8x2 + -9x2 = -1x2 4 + -20x + -1x2 = 0 Solving 4 + -20x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 20x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 20x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 20x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 20x + x2 = 0 + 4 20x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 20x + x2 = 4 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 4 + 100 Reorder the terms: 100 + 20x + x2 = 4 + 100 Combine like terms: 4 + 100 = 104 100 + 20x + x2 = 104 Factor a perfect square on the left side: (x + 10)(x + 10) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x + 10) equal to 10.198039027 and -10.198039027.Subproblem 1
x + 10 = 10.198039027 Simplifying x + 10 = 10.198039027 Reorder the terms: 10 + x = 10.198039027 Solving 10 + x = 10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 10.198039027 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.198039027 + -10 x = 10.198039027 + -10 Combine like terms: 10.198039027 + -10 = 0.198039027 x = 0.198039027 Simplifying x = 0.198039027Subproblem 2
x + 10 = -10.198039027 Simplifying x + 10 = -10.198039027 Reorder the terms: 10 + x = -10.198039027 Solving 10 + x = -10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -10.198039027 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.198039027 + -10 x = -10.198039027 + -10 Combine like terms: -10.198039027 + -10 = -20.198039027 x = -20.198039027 Simplifying x = -20.198039027Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.198039027, -20.198039027}
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