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Simplifying 225x2 + 11x + -210 = 0 Reorder the terms: -210 + 11x + 225x2 = 0 Solving -210 + 11x + 225x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 225 the coefficient of the squared term: Divide each side by '225'. -0.9333333333 + 0.04888888889x + x2 = 0 Move the constant term to the right: Add '0.9333333333' to each side of the equation. -0.9333333333 + 0.04888888889x + 0.9333333333 + x2 = 0 + 0.9333333333 Reorder the terms: -0.9333333333 + 0.9333333333 + 0.04888888889x + x2 = 0 + 0.9333333333 Combine like terms: -0.9333333333 + 0.9333333333 = 0.0000000000 0.0000000000 + 0.04888888889x + x2 = 0 + 0.9333333333 0.04888888889x + x2 = 0 + 0.9333333333 Combine like terms: 0 + 0.9333333333 = 0.9333333333 0.04888888889x + x2 = 0.9333333333 The x term is 0.04888888889x. Take half its coefficient (0.02444444445). Square it (0.0005975308645) and add it to both sides. Add '0.0005975308645' to each side of the equation. 0.04888888889x + 0.0005975308645 + x2 = 0.9333333333 + 0.0005975308645 Reorder the terms: 0.0005975308645 + 0.04888888889x + x2 = 0.9333333333 + 0.0005975308645 Combine like terms: 0.9333333333 + 0.0005975308645 = 0.9339308641645 0.0005975308645 + 0.04888888889x + x2 = 0.9339308641645 Factor a perfect square on the left side: (x + 0.02444444445)(x + 0.02444444445) = 0.9339308641645 Calculate the square root of the right side: 0.966400985 Break this problem into two subproblems by setting (x + 0.02444444445) equal to 0.966400985 and -0.966400985.Subproblem 1
x + 0.02444444445 = 0.966400985 Simplifying x + 0.02444444445 = 0.966400985 Reorder the terms: 0.02444444445 + x = 0.966400985 Solving 0.02444444445 + x = 0.966400985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02444444445' to each side of the equation. 0.02444444445 + -0.02444444445 + x = 0.966400985 + -0.02444444445 Combine like terms: 0.02444444445 + -0.02444444445 = 0.00000000000 0.00000000000 + x = 0.966400985 + -0.02444444445 x = 0.966400985 + -0.02444444445 Combine like terms: 0.966400985 + -0.02444444445 = 0.94195654055 x = 0.94195654055 Simplifying x = 0.94195654055Subproblem 2
x + 0.02444444445 = -0.966400985 Simplifying x + 0.02444444445 = -0.966400985 Reorder the terms: 0.02444444445 + x = -0.966400985 Solving 0.02444444445 + x = -0.966400985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02444444445' to each side of the equation. 0.02444444445 + -0.02444444445 + x = -0.966400985 + -0.02444444445 Combine like terms: 0.02444444445 + -0.02444444445 = 0.00000000000 0.00000000000 + x = -0.966400985 + -0.02444444445 x = -0.966400985 + -0.02444444445 Combine like terms: -0.966400985 + -0.02444444445 = -0.99084542945 x = -0.99084542945 Simplifying x = -0.99084542945Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.94195654055, -0.99084542945}
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