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Simplifying 25x2 + -24 + -9 = -7x2 + 12x + -18 Reorder the terms: -24 + -9 + 25x2 = -7x2 + 12x + -18 Combine like terms: -24 + -9 = -33 -33 + 25x2 = -7x2 + 12x + -18 Reorder the terms: -33 + 25x2 = -18 + 12x + -7x2 Solving -33 + 25x2 = -18 + 12x + -7x2 Solving for variable 'x'. Reorder the terms: -33 + 18 + -12x + 25x2 + 7x2 = -18 + 12x + -7x2 + 18 + -12x + 7x2 Combine like terms: -33 + 18 = -15 -15 + -12x + 25x2 + 7x2 = -18 + 12x + -7x2 + 18 + -12x + 7x2 Combine like terms: 25x2 + 7x2 = 32x2 -15 + -12x + 32x2 = -18 + 12x + -7x2 + 18 + -12x + 7x2 Reorder the terms: -15 + -12x + 32x2 = -18 + 18 + 12x + -12x + -7x2 + 7x2 Combine like terms: -18 + 18 = 0 -15 + -12x + 32x2 = 0 + 12x + -12x + -7x2 + 7x2 -15 + -12x + 32x2 = 12x + -12x + -7x2 + 7x2 Combine like terms: 12x + -12x = 0 -15 + -12x + 32x2 = 0 + -7x2 + 7x2 -15 + -12x + 32x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -15 + -12x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.46875 + -0.375x + x2 = 0 Move the constant term to the right: Add '0.46875' to each side of the equation. -0.46875 + -0.375x + 0.46875 + x2 = 0 + 0.46875 Reorder the terms: -0.46875 + 0.46875 + -0.375x + x2 = 0 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + -0.375x + x2 = 0 + 0.46875 -0.375x + x2 = 0 + 0.46875 Combine like terms: 0 + 0.46875 = 0.46875 -0.375x + x2 = 0.46875 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 0.46875 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 0.46875 + 0.03515625 Combine like terms: 0.46875 + 0.03515625 = 0.50390625 0.03515625 + -0.375x + x2 = 0.50390625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.50390625 Calculate the square root of the right side: 0.709863543 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.709863543 and -0.709863543.Subproblem 1
x + -0.1875 = 0.709863543 Simplifying x + -0.1875 = 0.709863543 Reorder the terms: -0.1875 + x = 0.709863543 Solving -0.1875 + x = 0.709863543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.709863543 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.709863543 + 0.1875 x = 0.709863543 + 0.1875 Combine like terms: 0.709863543 + 0.1875 = 0.897363543 x = 0.897363543 Simplifying x = 0.897363543Subproblem 2
x + -0.1875 = -0.709863543 Simplifying x + -0.1875 = -0.709863543 Reorder the terms: -0.1875 + x = -0.709863543 Solving -0.1875 + x = -0.709863543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.709863543 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.709863543 + 0.1875 x = -0.709863543 + 0.1875 Combine like terms: -0.709863543 + 0.1875 = -0.522363543 x = -0.522363543 Simplifying x = -0.522363543Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.897363543, -0.522363543}
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