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Simplifying 3.2x2 + 4.7x + 0.7 = 0 Reorder the terms: 0.7 + 4.7x + 3.2x2 = 0 Solving 0.7 + 4.7x + 3.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. 0.21875 + 1.46875x + x2 = 0 Move the constant term to the right: Add '-0.21875' to each side of the equation. 0.21875 + 1.46875x + -0.21875 + x2 = 0 + -0.21875 Reorder the terms: 0.21875 + -0.21875 + 1.46875x + x2 = 0 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + 1.46875x + x2 = 0 + -0.21875 1.46875x + x2 = 0 + -0.21875 Combine like terms: 0 + -0.21875 = -0.21875 1.46875x + x2 = -0.21875 The x term is 1.46875x. Take half its coefficient (0.734375). Square it (0.5393066406) and add it to both sides. Add '0.5393066406' to each side of the equation. 1.46875x + 0.5393066406 + x2 = -0.21875 + 0.5393066406 Reorder the terms: 0.5393066406 + 1.46875x + x2 = -0.21875 + 0.5393066406 Combine like terms: -0.21875 + 0.5393066406 = 0.3205566406 0.5393066406 + 1.46875x + x2 = 0.3205566406 Factor a perfect square on the left side: (x + 0.734375)(x + 0.734375) = 0.3205566406 Calculate the square root of the right side: 0.566177217 Break this problem into two subproblems by setting (x + 0.734375) equal to 0.566177217 and -0.566177217.Subproblem 1
x + 0.734375 = 0.566177217 Simplifying x + 0.734375 = 0.566177217 Reorder the terms: 0.734375 + x = 0.566177217 Solving 0.734375 + x = 0.566177217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.734375' to each side of the equation. 0.734375 + -0.734375 + x = 0.566177217 + -0.734375 Combine like terms: 0.734375 + -0.734375 = 0.000000 0.000000 + x = 0.566177217 + -0.734375 x = 0.566177217 + -0.734375 Combine like terms: 0.566177217 + -0.734375 = -0.168197783 x = -0.168197783 Simplifying x = -0.168197783Subproblem 2
x + 0.734375 = -0.566177217 Simplifying x + 0.734375 = -0.566177217 Reorder the terms: 0.734375 + x = -0.566177217 Solving 0.734375 + x = -0.566177217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.734375' to each side of the equation. 0.734375 + -0.734375 + x = -0.566177217 + -0.734375 Combine like terms: 0.734375 + -0.734375 = 0.000000 0.000000 + x = -0.566177217 + -0.734375 x = -0.566177217 + -0.734375 Combine like terms: -0.566177217 + -0.734375 = -1.300552217 x = -1.300552217 Simplifying x = -1.300552217Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.168197783, -1.300552217}
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