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Simplifying 0 = -4.9x2 + 12x + 300 Reorder the terms: 0 = 300 + 12x + -4.9x2 Solving 0 = 300 + 12x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -300 = -300 -300 + -12x + 4.9x2 = 300 + 12x + -4.9x2 + -300 + -12x + 4.9x2 Reorder the terms: -300 + -12x + 4.9x2 = 300 + -300 + 12x + -12x + -4.9x2 + 4.9x2 Combine like terms: 300 + -300 = 0 -300 + -12x + 4.9x2 = 0 + 12x + -12x + -4.9x2 + 4.9x2 -300 + -12x + 4.9x2 = 12x + -12x + -4.9x2 + 4.9x2 Combine like terms: 12x + -12x = 0 -300 + -12x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -300 + -12x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -300 + -12x + 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'. -61.2244898 + -2.448979592x + x2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + -2.448979592x + 61.2244898 + x2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + -2.448979592x + x2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + -2.448979592x + x2 = 0 + 61.2244898 -2.448979592x + x2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 -2.448979592x + x2 = 61.2244898 The x term is -2.448979592x. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592x + 1.499375261 + x2 = 61.2244898 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592x + x2 = 61.2244898 + 1.499375261 Combine like terms: 61.2244898 + 1.499375261 = 62.723865061 1.499375261 + -2.448979592x + x2 = 62.723865061 Factor a perfect square on the left side: (x + -1.224489796)(x + -1.224489796) = 62.723865061 Calculate the square root of the right side: 7.919839964 Break this problem into two subproblems by setting (x + -1.224489796) equal to 7.919839964 and -7.919839964.Subproblem 1
x + -1.224489796 = 7.919839964 Simplifying x + -1.224489796 = 7.919839964 Reorder the terms: -1.224489796 + x = 7.919839964 Solving -1.224489796 + x = 7.919839964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = 7.919839964 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = 7.919839964 + 1.224489796 x = 7.919839964 + 1.224489796 Combine like terms: 7.919839964 + 1.224489796 = 9.14432976 x = 9.14432976 Simplifying x = 9.14432976Subproblem 2
x + -1.224489796 = -7.919839964 Simplifying x + -1.224489796 = -7.919839964 Reorder the terms: -1.224489796 + x = -7.919839964 Solving -1.224489796 + x = -7.919839964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = -7.919839964 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = -7.919839964 + 1.224489796 x = -7.919839964 + 1.224489796 Combine like terms: -7.919839964 + 1.224489796 = -6.695350168 x = -6.695350168 Simplifying x = -6.695350168Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.14432976, -6.695350168}
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