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Simplifying -50x2 + 13 = 42x + -39 Reorder the terms: 13 + -50x2 = 42x + -39 Reorder the terms: 13 + -50x2 = -39 + 42x Solving 13 + -50x2 = -39 + 42x Solving for variable 'x'. Reorder the terms: 13 + 39 + -42x + -50x2 = -39 + 42x + 39 + -42x Combine like terms: 13 + 39 = 52 52 + -42x + -50x2 = -39 + 42x + 39 + -42x Reorder the terms: 52 + -42x + -50x2 = -39 + 39 + 42x + -42x Combine like terms: -39 + 39 = 0 52 + -42x + -50x2 = 0 + 42x + -42x 52 + -42x + -50x2 = 42x + -42x Combine like terms: 42x + -42x = 0 52 + -42x + -50x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(26 + -21x + -25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + -21x + -25x2)' equal to zero and attempt to solve: Simplifying 26 + -21x + -25x2 = 0 Solving 26 + -21x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -1.04 + 0.84x + x2 = 0 Move the constant term to the right: Add '1.04' to each side of the equation. -1.04 + 0.84x + 1.04 + x2 = 0 + 1.04 Reorder the terms: -1.04 + 1.04 + 0.84x + x2 = 0 + 1.04 Combine like terms: -1.04 + 1.04 = 0.00 0.00 + 0.84x + x2 = 0 + 1.04 0.84x + x2 = 0 + 1.04 Combine like terms: 0 + 1.04 = 1.04 0.84x + x2 = 1.04 The x term is 0.84x. Take half its coefficient (0.42). Square it (0.1764) and add it to both sides. Add '0.1764' to each side of the equation. 0.84x + 0.1764 + x2 = 1.04 + 0.1764 Reorder the terms: 0.1764 + 0.84x + x2 = 1.04 + 0.1764 Combine like terms: 1.04 + 0.1764 = 1.2164 0.1764 + 0.84x + x2 = 1.2164 Factor a perfect square on the left side: (x + 0.42)(x + 0.42) = 1.2164 Calculate the square root of the right side: 1.102905254 Break this problem into two subproblems by setting (x + 0.42) equal to 1.102905254 and -1.102905254.Subproblem 1
x + 0.42 = 1.102905254 Simplifying x + 0.42 = 1.102905254 Reorder the terms: 0.42 + x = 1.102905254 Solving 0.42 + x = 1.102905254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.42' to each side of the equation. 0.42 + -0.42 + x = 1.102905254 + -0.42 Combine like terms: 0.42 + -0.42 = 0.00 0.00 + x = 1.102905254 + -0.42 x = 1.102905254 + -0.42 Combine like terms: 1.102905254 + -0.42 = 0.682905254 x = 0.682905254 Simplifying x = 0.682905254Subproblem 2
x + 0.42 = -1.102905254 Simplifying x + 0.42 = -1.102905254 Reorder the terms: 0.42 + x = -1.102905254 Solving 0.42 + x = -1.102905254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.42' to each side of the equation. 0.42 + -0.42 + x = -1.102905254 + -0.42 Combine like terms: 0.42 + -0.42 = 0.00 0.00 + x = -1.102905254 + -0.42 x = -1.102905254 + -0.42 Combine like terms: -1.102905254 + -0.42 = -1.522905254 x = -1.522905254 Simplifying x = -1.522905254Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.682905254, -1.522905254}Solution
x = {0.682905254, -1.522905254}
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