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Simplifying -14 = 0.005x2 + -0.666x + 2.795 Reorder the terms: -14 = 2.795 + -0.666x + 0.005x2 Solving -14 = 2.795 + -0.666x + 0.005x2 Solving for variable 'x'. Combine like terms: -14 + -2.795 = -16.795 -16.795 + 0.666x + -0.005x2 = 2.795 + -0.666x + 0.005x2 + -2.795 + 0.666x + -0.005x2 Reorder the terms: -16.795 + 0.666x + -0.005x2 = 2.795 + -2.795 + -0.666x + 0.666x + 0.005x2 + -0.005x2 Combine like terms: 2.795 + -2.795 = 0.000 -16.795 + 0.666x + -0.005x2 = 0.000 + -0.666x + 0.666x + 0.005x2 + -0.005x2 -16.795 + 0.666x + -0.005x2 = -0.666x + 0.666x + 0.005x2 + -0.005x2 Combine like terms: -0.666x + 0.666x = 0.000 -16.795 + 0.666x + -0.005x2 = 0.000 + 0.005x2 + -0.005x2 -16.795 + 0.666x + -0.005x2 = 0.005x2 + -0.005x2 Combine like terms: 0.005x2 + -0.005x2 = 0.000 -16.795 + 0.666x + -0.005x2 = 0.000 Begin completing the square. Divide all terms by -0.005 the coefficient of the squared term: Divide each side by '-0.005'. 3359 + -133.2x + x2 = 0 Move the constant term to the right: Add '-3359' to each side of the equation. 3359 + -133.2x + -3359 + x2 = 0 + -3359 Reorder the terms: 3359 + -3359 + -133.2x + x2 = 0 + -3359 Combine like terms: 3359 + -3359 = 0 0 + -133.2x + x2 = 0 + -3359 -133.2x + x2 = 0 + -3359 Combine like terms: 0 + -3359 = -3359 -133.2x + x2 = -3359 The x term is -133.2x. Take half its coefficient (-66.6). Square it (4435.56) and add it to both sides. Add '4435.56' to each side of the equation. -133.2x + 4435.56 + x2 = -3359 + 4435.56 Reorder the terms: 4435.56 + -133.2x + x2 = -3359 + 4435.56 Combine like terms: -3359 + 4435.56 = 1076.56 4435.56 + -133.2x + x2 = 1076.56 Factor a perfect square on the left side: (x + -66.6)(x + -66.6) = 1076.56 Calculate the square root of the right side: 32.810973774 Break this problem into two subproblems by setting (x + -66.6) equal to 32.810973774 and -32.810973774.Subproblem 1
x + -66.6 = 32.810973774 Simplifying x + -66.6 = 32.810973774 Reorder the terms: -66.6 + x = 32.810973774 Solving -66.6 + x = 32.810973774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.6' to each side of the equation. -66.6 + 66.6 + x = 32.810973774 + 66.6 Combine like terms: -66.6 + 66.6 = 0.0 0.0 + x = 32.810973774 + 66.6 x = 32.810973774 + 66.6 Combine like terms: 32.810973774 + 66.6 = 99.410973774 x = 99.410973774 Simplifying x = 99.410973774Subproblem 2
x + -66.6 = -32.810973774 Simplifying x + -66.6 = -32.810973774 Reorder the terms: -66.6 + x = -32.810973774 Solving -66.6 + x = -32.810973774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.6' to each side of the equation. -66.6 + 66.6 + x = -32.810973774 + 66.6 Combine like terms: -66.6 + 66.6 = 0.0 0.0 + x = -32.810973774 + 66.6 x = -32.810973774 + 66.6 Combine like terms: -32.810973774 + 66.6 = 33.789026226 x = 33.789026226 Simplifying x = 33.789026226Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.410973774, 33.789026226}
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