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Simplifying 10 = -4.9x2 + 20x + 5 Reorder the terms: 10 = 5 + 20x + -4.9x2 Solving 10 = 5 + 20x + -4.9x2 Solving for variable 'x'. Combine like terms: 10 + -5 = 5 5 + -20x + 4.9x2 = 5 + 20x + -4.9x2 + -5 + -20x + 4.9x2 Reorder the terms: 5 + -20x + 4.9x2 = 5 + -5 + 20x + -20x + -4.9x2 + 4.9x2 Combine like terms: 5 + -5 = 0 5 + -20x + 4.9x2 = 0 + 20x + -20x + -4.9x2 + 4.9x2 5 + -20x + 4.9x2 = 20x + -20x + -4.9x2 + 4.9x2 Combine like terms: 20x + -20x = 0 5 + -20x + 4.9x2 = 0 + -4.9x2 + 4.9x2 5 + -20x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 5 + -20x + 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 + -4.081632653x + x2 = 0 Move the constant term to the right: Add '-1.020408163' to each side of the equation. 1.020408163 + -4.081632653x + -1.020408163 + x2 = 0 + -1.020408163 Reorder the terms: 1.020408163 + -1.020408163 + -4.081632653x + x2 = 0 + -1.020408163 Combine like terms: 1.020408163 + -1.020408163 = 0.000000000 0.000000000 + -4.081632653x + x2 = 0 + -1.020408163 -4.081632653x + x2 = 0 + -1.020408163 Combine like terms: 0 + -1.020408163 = -1.020408163 -4.081632653x + x2 = -1.020408163 The x term is -4.081632653x. Take half its coefficient (-2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. -4.081632653x + 4.164931281 + x2 = -1.020408163 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653x + x2 = -1.020408163 + 4.164931281 Combine like terms: -1.020408163 + 4.164931281 = 3.144523118 4.164931281 + -4.081632653x + x2 = 3.144523118 Factor a perfect square on the left side: (x + -2.040816327)(x + -2.040816327) = 3.144523118 Calculate the square root of the right side: 1.773280327 Break this problem into two subproblems by setting (x + -2.040816327) equal to 1.773280327 and -1.773280327.Subproblem 1
x + -2.040816327 = 1.773280327 Simplifying x + -2.040816327 = 1.773280327 Reorder the terms: -2.040816327 + x = 1.773280327 Solving -2.040816327 + x = 1.773280327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = 1.773280327 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 1.773280327 + 2.040816327 x = 1.773280327 + 2.040816327 Combine like terms: 1.773280327 + 2.040816327 = 3.814096654 x = 3.814096654 Simplifying x = 3.814096654Subproblem 2
x + -2.040816327 = -1.773280327 Simplifying x + -2.040816327 = -1.773280327 Reorder the terms: -2.040816327 + x = -1.773280327 Solving -2.040816327 + x = -1.773280327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = -1.773280327 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -1.773280327 + 2.040816327 x = -1.773280327 + 2.040816327 Combine like terms: -1.773280327 + 2.040816327 = 0.267536 x = 0.267536 Simplifying x = 0.267536Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.814096654, 0.267536}
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