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Simplifying -4.9x2 + 24x + 3 = 25 Reorder the terms: 3 + 24x + -4.9x2 = 25 Solving 3 + 24x + -4.9x2 = 25 Solving for variable 'x'. Reorder the terms: 3 + -25 + 24x + -4.9x2 = 25 + -25 Combine like terms: 3 + -25 = -22 -22 + 24x + -4.9x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -22 + 24x + -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'. 4.489795918 + -4.897959184x + x2 = 0 Move the constant term to the right: Add '-4.489795918' to each side of the equation. 4.489795918 + -4.897959184x + -4.489795918 + x2 = 0 + -4.489795918 Reorder the terms: 4.489795918 + -4.489795918 + -4.897959184x + x2 = 0 + -4.489795918 Combine like terms: 4.489795918 + -4.489795918 = 0.000000000 0.000000000 + -4.897959184x + x2 = 0 + -4.489795918 -4.897959184x + x2 = 0 + -4.489795918 Combine like terms: 0 + -4.489795918 = -4.489795918 -4.897959184x + x2 = -4.489795918 The x term is -4.897959184x. Take half its coefficient (-2.448979592). Square it (5.997501042) and add it to both sides. Add '5.997501042' to each side of the equation. -4.897959184x + 5.997501042 + x2 = -4.489795918 + 5.997501042 Reorder the terms: 5.997501042 + -4.897959184x + x2 = -4.489795918 + 5.997501042 Combine like terms: -4.489795918 + 5.997501042 = 1.507705124 5.997501042 + -4.897959184x + x2 = 1.507705124 Factor a perfect square on the left side: (x + -2.448979592)(x + -2.448979592) = 1.507705124 Calculate the square root of the right side: 1.227886446 Break this problem into two subproblems by setting (x + -2.448979592) equal to 1.227886446 and -1.227886446.Subproblem 1
x + -2.448979592 = 1.227886446 Simplifying x + -2.448979592 = 1.227886446 Reorder the terms: -2.448979592 + x = 1.227886446 Solving -2.448979592 + x = 1.227886446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.448979592' to each side of the equation. -2.448979592 + 2.448979592 + x = 1.227886446 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + x = 1.227886446 + 2.448979592 x = 1.227886446 + 2.448979592 Combine like terms: 1.227886446 + 2.448979592 = 3.676866038 x = 3.676866038 Simplifying x = 3.676866038Subproblem 2
x + -2.448979592 = -1.227886446 Simplifying x + -2.448979592 = -1.227886446 Reorder the terms: -2.448979592 + x = -1.227886446 Solving -2.448979592 + x = -1.227886446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.448979592' to each side of the equation. -2.448979592 + 2.448979592 + x = -1.227886446 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + x = -1.227886446 + 2.448979592 x = -1.227886446 + 2.448979592 Combine like terms: -1.227886446 + 2.448979592 = 1.221093146 x = 1.221093146 Simplifying x = 1.221093146Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.676866038, 1.221093146}
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