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Simplifying 19x2 + 19x + -450 = 0 Reorder the terms: -450 + 19x + 19x2 = 0 Solving -450 + 19x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -23.68421053 + x + x2 = 0 Move the constant term to the right: Add '23.68421053' to each side of the equation. -23.68421053 + x + 23.68421053 + x2 = 0 + 23.68421053 Reorder the terms: -23.68421053 + 23.68421053 + x + x2 = 0 + 23.68421053 Combine like terms: -23.68421053 + 23.68421053 = 0.00000000 0.00000000 + x + x2 = 0 + 23.68421053 x + x2 = 0 + 23.68421053 Combine like terms: 0 + 23.68421053 = 23.68421053 x + x2 = 23.68421053 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 23.68421053 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 23.68421053 + 0.25 Combine like terms: 23.68421053 + 0.25 = 23.93421053 1.25 + x2 = 23.93421053 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 23.93421053 Calculate the square root of the right side: 4.892260268 Break this problem into two subproblems by setting (x + 0.5) equal to 4.892260268 and -4.892260268.Subproblem 1
x + 0.5 = 4.892260268 Simplifying x + 0.5 = 4.892260268 Reorder the terms: 0.5 + x = 4.892260268 Solving 0.5 + x = 4.892260268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.892260268 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.892260268 + -0.5 x = 4.892260268 + -0.5 Combine like terms: 4.892260268 + -0.5 = 4.392260268 x = 4.392260268 Simplifying x = 4.392260268Subproblem 2
x + 0.5 = -4.892260268 Simplifying x + 0.5 = -4.892260268 Reorder the terms: 0.5 + x = -4.892260268 Solving 0.5 + x = -4.892260268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.892260268 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.892260268 + -0.5 x = -4.892260268 + -0.5 Combine like terms: -4.892260268 + -0.5 = -5.392260268 x = -5.392260268 Simplifying x = -5.392260268Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.392260268, -5.392260268}
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