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Simplifying -5 = -4.9x2 + 22x Reorder the terms: -5 = 22x + -4.9x2 Solving -5 = 22x + -4.9x2 Solving for variable 'x'. Reorder the terms: -5 + -22x + 4.9x2 = 22x + -22x + -4.9x2 + 4.9x2 Combine like terms: 22x + -22x = 0 -5 + -22x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -5 + -22x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -5 + -22x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.020408163 + -4.489795918x + x2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -4.489795918x + 1.020408163 + x2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -4.489795918x + x2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -4.489795918x + x2 = 0 + 1.020408163 -4.489795918x + x2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -4.489795918x + x2 = 1.020408163 The x term is -4.489795918x. Take half its coefficient (-2.244897959). Square it (5.039566846) and add it to both sides. Add '5.039566846' to each side of the equation. -4.489795918x + 5.039566846 + x2 = 1.020408163 + 5.039566846 Reorder the terms: 5.039566846 + -4.489795918x + x2 = 1.020408163 + 5.039566846 Combine like terms: 1.020408163 + 5.039566846 = 6.059975009 5.039566846 + -4.489795918x + x2 = 6.059975009 Factor a perfect square on the left side: (x + -2.244897959)(x + -2.244897959) = 6.059975009 Calculate the square root of the right side: 2.461701649 Break this problem into two subproblems by setting (x + -2.244897959) equal to 2.461701649 and -2.461701649.Subproblem 1
x + -2.244897959 = 2.461701649 Simplifying x + -2.244897959 = 2.461701649 Reorder the terms: -2.244897959 + x = 2.461701649 Solving -2.244897959 + x = 2.461701649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.244897959' to each side of the equation. -2.244897959 + 2.244897959 + x = 2.461701649 + 2.244897959 Combine like terms: -2.244897959 + 2.244897959 = 0.000000000 0.000000000 + x = 2.461701649 + 2.244897959 x = 2.461701649 + 2.244897959 Combine like terms: 2.461701649 + 2.244897959 = 4.706599608 x = 4.706599608 Simplifying x = 4.706599608Subproblem 2
x + -2.244897959 = -2.461701649 Simplifying x + -2.244897959 = -2.461701649 Reorder the terms: -2.244897959 + x = -2.461701649 Solving -2.244897959 + x = -2.461701649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.244897959' to each side of the equation. -2.244897959 + 2.244897959 + x = -2.461701649 + 2.244897959 Combine like terms: -2.244897959 + 2.244897959 = 0.000000000 0.000000000 + x = -2.461701649 + 2.244897959 x = -2.461701649 + 2.244897959 Combine like terms: -2.461701649 + 2.244897959 = -0.21680369 x = -0.21680369 Simplifying x = -0.21680369Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.706599608, -0.21680369}
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