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Simplifying -4.9x2 + 32x + 0.2 = 15 Reorder the terms: 0.2 + 32x + -4.9x2 = 15 Solving 0.2 + 32x + -4.9x2 = 15 Solving for variable 'x'. Reorder the terms: 0.2 + -15 + 32x + -4.9x2 = 15 + -15 Combine like terms: 0.2 + -15 = -14.8 -14.8 + 32x + -4.9x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -14.8 + 32x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 3.020408163 + -6.530612245x + x2 = 0 Move the constant term to the right: Add '-3.020408163' to each side of the equation. 3.020408163 + -6.530612245x + -3.020408163 + x2 = 0 + -3.020408163 Reorder the terms: 3.020408163 + -3.020408163 + -6.530612245x + x2 = 0 + -3.020408163 Combine like terms: 3.020408163 + -3.020408163 = 0.000000000 0.000000000 + -6.530612245x + x2 = 0 + -3.020408163 -6.530612245x + x2 = 0 + -3.020408163 Combine like terms: 0 + -3.020408163 = -3.020408163 -6.530612245x + x2 = -3.020408163 The x term is -6.530612245x. Take half its coefficient (-3.265306123). Square it (10.66222408) and add it to both sides. Add '10.66222408' to each side of the equation. -6.530612245x + 10.66222408 + x2 = -3.020408163 + 10.66222408 Reorder the terms: 10.66222408 + -6.530612245x + x2 = -3.020408163 + 10.66222408 Combine like terms: -3.020408163 + 10.66222408 = 7.641815917 10.66222408 + -6.530612245x + x2 = 7.641815917 Factor a perfect square on the left side: (x + -3.265306123)(x + -3.265306123) = 7.641815917 Calculate the square root of the right side: 2.764383461 Break this problem into two subproblems by setting (x + -3.265306123) equal to 2.764383461 and -2.764383461.Subproblem 1
x + -3.265306123 = 2.764383461 Simplifying x + -3.265306123 = 2.764383461 Reorder the terms: -3.265306123 + x = 2.764383461 Solving -3.265306123 + x = 2.764383461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.265306123' to each side of the equation. -3.265306123 + 3.265306123 + x = 2.764383461 + 3.265306123 Combine like terms: -3.265306123 + 3.265306123 = 0.000000000 0.000000000 + x = 2.764383461 + 3.265306123 x = 2.764383461 + 3.265306123 Combine like terms: 2.764383461 + 3.265306123 = 6.029689584 x = 6.029689584 Simplifying x = 6.029689584Subproblem 2
x + -3.265306123 = -2.764383461 Simplifying x + -3.265306123 = -2.764383461 Reorder the terms: -3.265306123 + x = -2.764383461 Solving -3.265306123 + x = -2.764383461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.265306123' to each side of the equation. -3.265306123 + 3.265306123 + x = -2.764383461 + 3.265306123 Combine like terms: -3.265306123 + 3.265306123 = 0.000000000 0.000000000 + x = -2.764383461 + 3.265306123 x = -2.764383461 + 3.265306123 Combine like terms: -2.764383461 + 3.265306123 = 0.500922662 x = 0.500922662 Simplifying x = 0.500922662Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.029689584, 0.500922662}
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