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Simplifying 0.0029x2 + -0.289x + 6.9 = 1000 Reorder the terms: 6.9 + -0.289x + 0.0029x2 = 1000 Solving 6.9 + -0.289x + 0.0029x2 = 1000 Solving for variable 'x'. Reorder the terms: 6.9 + -1000 + -0.289x + 0.0029x2 = 1000 + -1000 Combine like terms: 6.9 + -1000 = -993.1 -993.1 + -0.289x + 0.0029x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -993.1 + -0.289x + 0.0029x2 = 0 Begin completing the square. Divide all terms by 0.0029 the coefficient of the squared term: Divide each side by '0.0029'. -342448.2759 + -99.65517241x + x2 = 0 Move the constant term to the right: Add '342448.2759' to each side of the equation. -342448.2759 + -99.65517241x + 342448.2759 + x2 = 0 + 342448.2759 Reorder the terms: -342448.2759 + 342448.2759 + -99.65517241x + x2 = 0 + 342448.2759 Combine like terms: -342448.2759 + 342448.2759 = 0.0000 0.0000 + -99.65517241x + x2 = 0 + 342448.2759 -99.65517241x + x2 = 0 + 342448.2759 Combine like terms: 0 + 342448.2759 = 342448.2759 -99.65517241x + x2 = 342448.2759 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 = 342448.2759 + 2482.788348 Reorder the terms: 2482.788348 + -99.65517241x + x2 = 342448.2759 + 2482.788348 Combine like terms: 342448.2759 + 2482.788348 = 344931.064248 2482.788348 + -99.65517241x + x2 = 344931.064248 Factor a perfect square on the left side: (x + -49.82758621)(x + -49.82758621) = 344931.064248 Calculate the square root of the right side: 587.308321283 Break this problem into two subproblems by setting (x + -49.82758621) equal to 587.308321283 and -587.308321283.Subproblem 1
x + -49.82758621 = 587.308321283 Simplifying x + -49.82758621 = 587.308321283 Reorder the terms: -49.82758621 + x = 587.308321283 Solving -49.82758621 + x = 587.308321283 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 = 587.308321283 + 49.82758621 Combine like terms: -49.82758621 + 49.82758621 = 0.00000000 0.00000000 + x = 587.308321283 + 49.82758621 x = 587.308321283 + 49.82758621 Combine like terms: 587.308321283 + 49.82758621 = 637.135907493 x = 637.135907493 Simplifying x = 637.135907493Subproblem 2
x + -49.82758621 = -587.308321283 Simplifying x + -49.82758621 = -587.308321283 Reorder the terms: -49.82758621 + x = -587.308321283 Solving -49.82758621 + x = -587.308321283 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 = -587.308321283 + 49.82758621 Combine like terms: -49.82758621 + 49.82758621 = 0.00000000 0.00000000 + x = -587.308321283 + 49.82758621 x = -587.308321283 + 49.82758621 Combine like terms: -587.308321283 + 49.82758621 = -537.480735073 x = -537.480735073 Simplifying x = -537.480735073Solution
The solution to the problem is based on the solutions from the subproblems. x = {637.135907493, -537.480735073}
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