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Simplifying 325x + -170.0562(1 + x2) = -65 325x + (1 * -170.0562 + x2 * -170.0562) = -65 325x + (-170.0562 + -170.0562x2) = -65 Reorder the terms: -170.0562 + 325x + -170.0562x2 = -65 Solving -170.0562 + 325x + -170.0562x2 = -65 Solving for variable 'x'. Reorder the terms: -170.0562 + 65 + 325x + -170.0562x2 = -65 + 65 Combine like terms: -170.0562 + 65 = -105.0562 -105.0562 + 325x + -170.0562x2 = -65 + 65 Combine like terms: -65 + 65 = 0 -105.0562 + 325x + -170.0562x2 = 0 Begin completing the square. Divide all terms by -170.0562 the coefficient of the squared term: Divide each side by '-170.0562'. 0.6177734184 + -1.911132908x + x2 = 0 Move the constant term to the right: Add '-0.6177734184' to each side of the equation. 0.6177734184 + -1.911132908x + -0.6177734184 + x2 = 0 + -0.6177734184 Reorder the terms: 0.6177734184 + -0.6177734184 + -1.911132908x + x2 = 0 + -0.6177734184 Combine like terms: 0.6177734184 + -0.6177734184 = 0.0000000000 0.0000000000 + -1.911132908x + x2 = 0 + -0.6177734184 -1.911132908x + x2 = 0 + -0.6177734184 Combine like terms: 0 + -0.6177734184 = -0.6177734184 -1.911132908x + x2 = -0.6177734184 The x term is -1.911132908x. Take half its coefficient (-0.955566454). Square it (0.9131072480) and add it to both sides. Add '0.9131072480' to each side of the equation. -1.911132908x + 0.9131072480 + x2 = -0.6177734184 + 0.9131072480 Reorder the terms: 0.9131072480 + -1.911132908x + x2 = -0.6177734184 + 0.9131072480 Combine like terms: -0.6177734184 + 0.9131072480 = 0.2953338296 0.9131072480 + -1.911132908x + x2 = 0.2953338296 Factor a perfect square on the left side: (x + -0.955566454)(x + -0.955566454) = 0.2953338296 Calculate the square root of the right side: 0.543446253 Break this problem into two subproblems by setting (x + -0.955566454) equal to 0.543446253 and -0.543446253.Subproblem 1
x + -0.955566454 = 0.543446253 Simplifying x + -0.955566454 = 0.543446253 Reorder the terms: -0.955566454 + x = 0.543446253 Solving -0.955566454 + x = 0.543446253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.955566454' to each side of the equation. -0.955566454 + 0.955566454 + x = 0.543446253 + 0.955566454 Combine like terms: -0.955566454 + 0.955566454 = 0.000000000 0.000000000 + x = 0.543446253 + 0.955566454 x = 0.543446253 + 0.955566454 Combine like terms: 0.543446253 + 0.955566454 = 1.499012707 x = 1.499012707 Simplifying x = 1.499012707Subproblem 2
x + -0.955566454 = -0.543446253 Simplifying x + -0.955566454 = -0.543446253 Reorder the terms: -0.955566454 + x = -0.543446253 Solving -0.955566454 + x = -0.543446253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.955566454' to each side of the equation. -0.955566454 + 0.955566454 + x = -0.543446253 + 0.955566454 Combine like terms: -0.955566454 + 0.955566454 = 0.000000000 0.000000000 + x = -0.543446253 + 0.955566454 x = -0.543446253 + 0.955566454 Combine like terms: -0.543446253 + 0.955566454 = 0.412120201 x = 0.412120201 Simplifying x = 0.412120201Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.499012707, 0.412120201}
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