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Simplifying 4x2 + 1.5x + -21 = 0 Reorder the terms: -21 + 1.5x + 4x2 = 0 Solving -21 + 1.5x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 0.375x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 0.375x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 0.375x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 0.375x + x2 = 0 + 5.25 0.375x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 0.375x + x2 = 5.25 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 5.25 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 5.25 + 0.03515625 Combine like terms: 5.25 + 0.03515625 = 5.28515625 0.03515625 + 0.375x + x2 = 5.28515625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 5.28515625 Calculate the square root of the right side: 2.29894677 Break this problem into two subproblems by setting (x + 0.1875) equal to 2.29894677 and -2.29894677.Subproblem 1
x + 0.1875 = 2.29894677 Simplifying x + 0.1875 = 2.29894677 Reorder the terms: 0.1875 + x = 2.29894677 Solving 0.1875 + x = 2.29894677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 2.29894677 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 2.29894677 + -0.1875 x = 2.29894677 + -0.1875 Combine like terms: 2.29894677 + -0.1875 = 2.11144677 x = 2.11144677 Simplifying x = 2.11144677Subproblem 2
x + 0.1875 = -2.29894677 Simplifying x + 0.1875 = -2.29894677 Reorder the terms: 0.1875 + x = -2.29894677 Solving 0.1875 + x = -2.29894677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -2.29894677 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -2.29894677 + -0.1875 x = -2.29894677 + -0.1875 Combine like terms: -2.29894677 + -0.1875 = -2.48644677 x = -2.48644677 Simplifying x = -2.48644677Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.11144677, -2.48644677}
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