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Simplifying (0.303)(0.760 + -1x) = x2 (0.760 * 0.303 + -1x * 0.303) = x2 (0.23028 + -0.303x) = x2 Solving 0.23028 + -0.303x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.23028 + -0.303x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.23028 + 0.303x + x2 = 0 Move the constant term to the right: Add '0.23028' to each side of the equation. -0.23028 + 0.303x + 0.23028 + x2 = 0 + 0.23028 Reorder the terms: -0.23028 + 0.23028 + 0.303x + x2 = 0 + 0.23028 Combine like terms: -0.23028 + 0.23028 = 0.00000 0.00000 + 0.303x + x2 = 0 + 0.23028 0.303x + x2 = 0 + 0.23028 Combine like terms: 0 + 0.23028 = 0.23028 0.303x + x2 = 0.23028 The x term is 0.303x. Take half its coefficient (0.1515). Square it (0.02295225) and add it to both sides. Add '0.02295225' to each side of the equation. 0.303x + 0.02295225 + x2 = 0.23028 + 0.02295225 Reorder the terms: 0.02295225 + 0.303x + x2 = 0.23028 + 0.02295225 Combine like terms: 0.23028 + 0.02295225 = 0.25323225 0.02295225 + 0.303x + x2 = 0.25323225 Factor a perfect square on the left side: (x + 0.1515)(x + 0.1515) = 0.25323225 Calculate the square root of the right side: 0.50322187 Break this problem into two subproblems by setting (x + 0.1515) equal to 0.50322187 and -0.50322187.Subproblem 1
x + 0.1515 = 0.50322187 Simplifying x + 0.1515 = 0.50322187 Reorder the terms: 0.1515 + x = 0.50322187 Solving 0.1515 + x = 0.50322187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1515' to each side of the equation. 0.1515 + -0.1515 + x = 0.50322187 + -0.1515 Combine like terms: 0.1515 + -0.1515 = 0.0000 0.0000 + x = 0.50322187 + -0.1515 x = 0.50322187 + -0.1515 Combine like terms: 0.50322187 + -0.1515 = 0.35172187 x = 0.35172187 Simplifying x = 0.35172187Subproblem 2
x + 0.1515 = -0.50322187 Simplifying x + 0.1515 = -0.50322187 Reorder the terms: 0.1515 + x = -0.50322187 Solving 0.1515 + x = -0.50322187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1515' to each side of the equation. 0.1515 + -0.1515 + x = -0.50322187 + -0.1515 Combine like terms: 0.1515 + -0.1515 = 0.0000 0.0000 + x = -0.50322187 + -0.1515 x = -0.50322187 + -0.1515 Combine like terms: -0.50322187 + -0.1515 = -0.65472187 x = -0.65472187 Simplifying x = -0.65472187Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.35172187, -0.65472187}
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