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Simplifying 5x2 + -456245x = 12 Reorder the terms: -456245x + 5x2 = 12 Solving -456245x + 5x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -456245x + 5x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -456245x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -91249x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -91249x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -91249x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -91249x + x2 = 0 + 2.4 -91249x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -91249x + x2 = 2.4 The x term is -91249x. Take half its coefficient (-45624.5). Square it (2081595000) and add it to both sides. Add '2081595000' to each side of the equation. -91249x + 2081595000 + x2 = 2.4 + 2081595000 Reorder the terms: 2081595000 + -91249x + x2 = 2.4 + 2081595000 Combine like terms: 2.4 + 2081595000 = 2081595002.4 2081595000 + -91249x + x2 = 2081595002.4 Factor a perfect square on the left side: (x + -45624.5)(x + -45624.5) = 2081595002.4 Calculate the square root of the right side: 45624.500023562 Break this problem into two subproblems by setting (x + -45624.5) equal to 45624.500023562 and -45624.500023562.Subproblem 1
x + -45624.5 = 45624.500023562 Simplifying x + -45624.5 = 45624.500023562 Reorder the terms: -45624.5 + x = 45624.500023562 Solving -45624.5 + x = 45624.500023562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45624.5' to each side of the equation. -45624.5 + 45624.5 + x = 45624.500023562 + 45624.5 Combine like terms: -45624.5 + 45624.5 = 0.0 0.0 + x = 45624.500023562 + 45624.5 x = 45624.500023562 + 45624.5 Combine like terms: 45624.500023562 + 45624.5 = 91249.000023562 x = 91249.000023562 Simplifying x = 91249.000023562Subproblem 2
x + -45624.5 = -45624.500023562 Simplifying x + -45624.5 = -45624.500023562 Reorder the terms: -45624.5 + x = -45624.500023562 Solving -45624.5 + x = -45624.500023562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45624.5' to each side of the equation. -45624.5 + 45624.5 + x = -45624.500023562 + 45624.5 Combine like terms: -45624.5 + 45624.5 = 0.0 0.0 + x = -45624.500023562 + 45624.5 x = -45624.500023562 + 45624.5 Combine like terms: -45624.500023562 + 45624.5 = -0.000023562 x = -0.000023562 Simplifying x = -0.000023562Solution
The solution to the problem is based on the solutions from the subproblems. x = {91249.000023562, -0.000023562}
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