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Simplifying x2 + 3x + -670 = 0 Reorder the terms: -670 + 3x + x2 = 0 Solving -670 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '670' to each side of the equation. -670 + 3x + 670 + x2 = 0 + 670 Reorder the terms: -670 + 670 + 3x + x2 = 0 + 670 Combine like terms: -670 + 670 = 0 0 + 3x + x2 = 0 + 670 3x + x2 = 0 + 670 Combine like terms: 0 + 670 = 670 3x + x2 = 670 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 670 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 670 + 2.25 Combine like terms: 670 + 2.25 = 672.25 2.25 + 3x + x2 = 672.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 672.25 Calculate the square root of the right side: 25.927784325 Break this problem into two subproblems by setting (x + 1.5) equal to 25.927784325 and -25.927784325.Subproblem 1
x + 1.5 = 25.927784325 Simplifying x + 1.5 = 25.927784325 Reorder the terms: 1.5 + x = 25.927784325 Solving 1.5 + x = 25.927784325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 25.927784325 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 25.927784325 + -1.5 x = 25.927784325 + -1.5 Combine like terms: 25.927784325 + -1.5 = 24.427784325 x = 24.427784325 Simplifying x = 24.427784325Subproblem 2
x + 1.5 = -25.927784325 Simplifying x + 1.5 = -25.927784325 Reorder the terms: 1.5 + x = -25.927784325 Solving 1.5 + x = -25.927784325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -25.927784325 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -25.927784325 + -1.5 x = -25.927784325 + -1.5 Combine like terms: -25.927784325 + -1.5 = -27.427784325 x = -27.427784325 Simplifying x = -27.427784325Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.427784325, -27.427784325}
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