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Simplifying 0 = -4.9x2 + 50x + 150 Reorder the terms: 0 = 150 + 50x + -4.9x2 Solving 0 = 150 + 50x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -150 = -150 -150 + -50x + 4.9x2 = 150 + 50x + -4.9x2 + -150 + -50x + 4.9x2 Reorder the terms: -150 + -50x + 4.9x2 = 150 + -150 + 50x + -50x + -4.9x2 + 4.9x2 Combine like terms: 150 + -150 = 0 -150 + -50x + 4.9x2 = 0 + 50x + -50x + -4.9x2 + 4.9x2 -150 + -50x + 4.9x2 = 50x + -50x + -4.9x2 + 4.9x2 Combine like terms: 50x + -50x = 0 -150 + -50x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -150 + -50x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -150 + -50x + 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'. -30.6122449 + -10.20408163x + x2 = 0 Move the constant term to the right: Add '30.6122449' to each side of the equation. -30.6122449 + -10.20408163x + 30.6122449 + x2 = 0 + 30.6122449 Reorder the terms: -30.6122449 + 30.6122449 + -10.20408163x + x2 = 0 + 30.6122449 Combine like terms: -30.6122449 + 30.6122449 = 0.0000000 0.0000000 + -10.20408163x + x2 = 0 + 30.6122449 -10.20408163x + x2 = 0 + 30.6122449 Combine like terms: 0 + 30.6122449 = 30.6122449 -10.20408163x + x2 = 30.6122449 The x term is -10.20408163x. Take half its coefficient (-5.102040815). Square it (26.03082048) and add it to both sides. Add '26.03082048' to each side of the equation. -10.20408163x + 26.03082048 + x2 = 30.6122449 + 26.03082048 Reorder the terms: 26.03082048 + -10.20408163x + x2 = 30.6122449 + 26.03082048 Combine like terms: 30.6122449 + 26.03082048 = 56.64306538 26.03082048 + -10.20408163x + x2 = 56.64306538 Factor a perfect square on the left side: (x + -5.102040815)(x + -5.102040815) = 56.64306538 Calculate the square root of the right side: 7.52615874 Break this problem into two subproblems by setting (x + -5.102040815) equal to 7.52615874 and -7.52615874.Subproblem 1
x + -5.102040815 = 7.52615874 Simplifying x + -5.102040815 = 7.52615874 Reorder the terms: -5.102040815 + x = 7.52615874 Solving -5.102040815 + x = 7.52615874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + x = 7.52615874 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = 7.52615874 + 5.102040815 x = 7.52615874 + 5.102040815 Combine like terms: 7.52615874 + 5.102040815 = 12.628199555 x = 12.628199555 Simplifying x = 12.628199555Subproblem 2
x + -5.102040815 = -7.52615874 Simplifying x + -5.102040815 = -7.52615874 Reorder the terms: -5.102040815 + x = -7.52615874 Solving -5.102040815 + x = -7.52615874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + x = -7.52615874 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = -7.52615874 + 5.102040815 x = -7.52615874 + 5.102040815 Combine like terms: -7.52615874 + 5.102040815 = -2.424117925 x = -2.424117925 Simplifying x = -2.424117925Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.628199555, -2.424117925}
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