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Simplifying 4x2 + 5.4x + -0.06 = 0 Reorder the terms: -0.06 + 5.4x + 4x2 = 0 Solving -0.06 + 5.4x + 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'. -0.015 + 1.35x + x2 = 0 Move the constant term to the right: Add '0.015' to each side of the equation. -0.015 + 1.35x + 0.015 + x2 = 0 + 0.015 Reorder the terms: -0.015 + 0.015 + 1.35x + x2 = 0 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + 1.35x + x2 = 0 + 0.015 1.35x + x2 = 0 + 0.015 Combine like terms: 0 + 0.015 = 0.015 1.35x + x2 = 0.015 The x term is 1.35x. Take half its coefficient (0.675). Square it (0.455625) and add it to both sides. Add '0.455625' to each side of the equation. 1.35x + 0.455625 + x2 = 0.015 + 0.455625 Reorder the terms: 0.455625 + 1.35x + x2 = 0.015 + 0.455625 Combine like terms: 0.015 + 0.455625 = 0.470625 0.455625 + 1.35x + x2 = 0.470625 Factor a perfect square on the left side: (x + 0.675)(x + 0.675) = 0.470625 Calculate the square root of the right side: 0.686021137 Break this problem into two subproblems by setting (x + 0.675) equal to 0.686021137 and -0.686021137.Subproblem 1
x + 0.675 = 0.686021137 Simplifying x + 0.675 = 0.686021137 Reorder the terms: 0.675 + x = 0.686021137 Solving 0.675 + x = 0.686021137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.675' to each side of the equation. 0.675 + -0.675 + x = 0.686021137 + -0.675 Combine like terms: 0.675 + -0.675 = 0.000 0.000 + x = 0.686021137 + -0.675 x = 0.686021137 + -0.675 Combine like terms: 0.686021137 + -0.675 = 0.011021137 x = 0.011021137 Simplifying x = 0.011021137Subproblem 2
x + 0.675 = -0.686021137 Simplifying x + 0.675 = -0.686021137 Reorder the terms: 0.675 + x = -0.686021137 Solving 0.675 + x = -0.686021137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.675' to each side of the equation. 0.675 + -0.675 + x = -0.686021137 + -0.675 Combine like terms: 0.675 + -0.675 = 0.000 0.000 + x = -0.686021137 + -0.675 x = -0.686021137 + -0.675 Combine like terms: -0.686021137 + -0.675 = -1.361021137 x = -1.361021137 Simplifying x = -1.361021137Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.011021137, -1.361021137}
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