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Simplifying 0.0029x2 + -0.289x + 6.9 = 0 Reorder the terms: 6.9 + -0.289x + 0.0029x2 = 0 Solving 6.9 + -0.289x + 0.0029x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0029 the coefficient of the squared term: Divide each side by '0.0029'. 2379.310345 + -99.65517241x + x2 = 0 Move the constant term to the right: Add '-2379.310345' to each side of the equation. 2379.310345 + -99.65517241x + -2379.310345 + x2 = 0 + -2379.310345 Reorder the terms: 2379.310345 + -2379.310345 + -99.65517241x + x2 = 0 + -2379.310345 Combine like terms: 2379.310345 + -2379.310345 = 0.000000 0.000000 + -99.65517241x + x2 = 0 + -2379.310345 -99.65517241x + x2 = 0 + -2379.310345 Combine like terms: 0 + -2379.310345 = -2379.310345 -99.65517241x + x2 = -2379.310345 The x term is -99.65517241x. Take half its coefficient (-49.82758621). Square it (2482.788348) and add it to both sides. Add '2482.788348' to each side of the equation. -99.65517241x + 2482.788348 + x2 = -2379.310345 + 2482.788348 Reorder the terms: 2482.788348 + -99.65517241x + x2 = -2379.310345 + 2482.788348 Combine like terms: -2379.310345 + 2482.788348 = 103.478003 2482.788348 + -99.65517241x + x2 = 103.478003 Factor a perfect square on the left side: (x + -49.82758621)(x + -49.82758621) = 103.478003 Calculate the square root of the right side: 10.172413824 Break this problem into two subproblems by setting (x + -49.82758621) equal to 10.172413824 and -10.172413824.Subproblem 1
x + -49.82758621 = 10.172413824 Simplifying x + -49.82758621 = 10.172413824 Reorder the terms: -49.82758621 + x = 10.172413824 Solving -49.82758621 + x = 10.172413824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.82758621' to each side of the equation. -49.82758621 + 49.82758621 + x = 10.172413824 + 49.82758621 Combine like terms: -49.82758621 + 49.82758621 = 0.00000000 0.00000000 + x = 10.172413824 + 49.82758621 x = 10.172413824 + 49.82758621 Combine like terms: 10.172413824 + 49.82758621 = 60.000000034 x = 60.000000034 Simplifying x = 60.000000034Subproblem 2
x + -49.82758621 = -10.172413824 Simplifying x + -49.82758621 = -10.172413824 Reorder the terms: -49.82758621 + x = -10.172413824 Solving -49.82758621 + x = -10.172413824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.82758621' to each side of the equation. -49.82758621 + 49.82758621 + x = -10.172413824 + 49.82758621 Combine like terms: -49.82758621 + 49.82758621 = 0.00000000 0.00000000 + x = -10.172413824 + 49.82758621 x = -10.172413824 + 49.82758621 Combine like terms: -10.172413824 + 49.82758621 = 39.655172386 x = 39.655172386 Simplifying x = 39.655172386Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.000000034, 39.655172386}
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