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Simplifying -1.2x2 + 2.9x + 5 = 2.6 Reorder the terms: 5 + 2.9x + -1.2x2 = 2.6 Solving 5 + 2.9x + -1.2x2 = 2.6 Solving for variable 'x'. Reorder the terms: 5 + -2.6 + 2.9x + -1.2x2 = 2.6 + -2.6 Combine like terms: 5 + -2.6 = 2.4 2.4 + 2.9x + -1.2x2 = 2.6 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 2.4 + 2.9x + -1.2x2 = 0.0 Begin completing the square. Divide all terms by -1.2 the coefficient of the squared term: Divide each side by '-1.2'. -2 + -2.416666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.416666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2.416666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.416666667x + x2 = 0 + 2 -2.416666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.416666667x + x2 = 2 The x term is -2.416666667x. Take half its coefficient (-1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. -2.416666667x + 1.460069446 + x2 = 2 + 1.460069446 Reorder the terms: 1.460069446 + -2.416666667x + x2 = 2 + 1.460069446 Combine like terms: 2 + 1.460069446 = 3.460069446 1.460069446 + -2.416666667x + x2 = 3.460069446 Factor a perfect square on the left side: (x + -1.208333334)(x + -1.208333334) = 3.460069446 Calculate the square root of the right side: 1.860126191 Break this problem into two subproblems by setting (x + -1.208333334) equal to 1.860126191 and -1.860126191.Subproblem 1
x + -1.208333334 = 1.860126191 Simplifying x + -1.208333334 = 1.860126191 Reorder the terms: -1.208333334 + x = 1.860126191 Solving -1.208333334 + x = 1.860126191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = 1.860126191 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = 1.860126191 + 1.208333334 x = 1.860126191 + 1.208333334 Combine like terms: 1.860126191 + 1.208333334 = 3.068459525 x = 3.068459525 Simplifying x = 3.068459525Subproblem 2
x + -1.208333334 = -1.860126191 Simplifying x + -1.208333334 = -1.860126191 Reorder the terms: -1.208333334 + x = -1.860126191 Solving -1.208333334 + x = -1.860126191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = -1.860126191 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = -1.860126191 + 1.208333334 x = -1.860126191 + 1.208333334 Combine like terms: -1.860126191 + 1.208333334 = -0.651792857 x = -0.651792857 Simplifying x = -0.651792857Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.068459525, -0.651792857}
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