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Simplifying 0 = -0.064 + 0.151x + x2 Solving 0 = -0.064 + 0.151x + x2 Solving for variable 'x'. Combine like terms: 0 + 0.064 = 0.064 0.064 + -0.151x + -1x2 = -0.064 + 0.151x + x2 + 0.064 + -0.151x + -1x2 Reorder the terms: 0.064 + -0.151x + -1x2 = -0.064 + 0.064 + 0.151x + -0.151x + x2 + -1x2 Combine like terms: -0.064 + 0.064 = 0.000 0.064 + -0.151x + -1x2 = 0.000 + 0.151x + -0.151x + x2 + -1x2 0.064 + -0.151x + -1x2 = 0.151x + -0.151x + x2 + -1x2 Combine like terms: 0.151x + -0.151x = 0.000 0.064 + -0.151x + -1x2 = 0.000 + x2 + -1x2 0.064 + -0.151x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.064 + -0.151x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.064 + 0.151x + x2 = 0 Move the constant term to the right: Add '0.064' to each side of the equation. -0.064 + 0.151x + 0.064 + x2 = 0 + 0.064 Reorder the terms: -0.064 + 0.064 + 0.151x + x2 = 0 + 0.064 Combine like terms: -0.064 + 0.064 = 0.000 0.000 + 0.151x + x2 = 0 + 0.064 0.151x + x2 = 0 + 0.064 Combine like terms: 0 + 0.064 = 0.064 0.151x + x2 = 0.064 The x term is 0.151x. Take half its coefficient (0.0755). Square it (0.00570025) and add it to both sides. Add '0.00570025' to each side of the equation. 0.151x + 0.00570025 + x2 = 0.064 + 0.00570025 Reorder the terms: 0.00570025 + 0.151x + x2 = 0.064 + 0.00570025 Combine like terms: 0.064 + 0.00570025 = 0.06970025 0.00570025 + 0.151x + x2 = 0.06970025 Factor a perfect square on the left side: (x + 0.0755)(x + 0.0755) = 0.06970025 Calculate the square root of the right side: 0.264008049 Break this problem into two subproblems by setting (x + 0.0755) equal to 0.264008049 and -0.264008049.Subproblem 1
x + 0.0755 = 0.264008049 Simplifying x + 0.0755 = 0.264008049 Reorder the terms: 0.0755 + x = 0.264008049 Solving 0.0755 + x = 0.264008049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0755' to each side of the equation. 0.0755 + -0.0755 + x = 0.264008049 + -0.0755 Combine like terms: 0.0755 + -0.0755 = 0.0000 0.0000 + x = 0.264008049 + -0.0755 x = 0.264008049 + -0.0755 Combine like terms: 0.264008049 + -0.0755 = 0.188508049 x = 0.188508049 Simplifying x = 0.188508049Subproblem 2
x + 0.0755 = -0.264008049 Simplifying x + 0.0755 = -0.264008049 Reorder the terms: 0.0755 + x = -0.264008049 Solving 0.0755 + x = -0.264008049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0755' to each side of the equation. 0.0755 + -0.0755 + x = -0.264008049 + -0.0755 Combine like terms: 0.0755 + -0.0755 = 0.0000 0.0000 + x = -0.264008049 + -0.0755 x = -0.264008049 + -0.0755 Combine like terms: -0.264008049 + -0.0755 = -0.339508049 x = -0.339508049 Simplifying x = -0.339508049Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.188508049, -0.339508049}
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