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Simplifying 4x2 + 12x + -1.6 = 0 Reorder the terms: -1.6 + 12x + 4x2 = 0 Solving -1.6 + 12x + 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'. -0.4 + 3x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 3x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 3x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 3x + x2 = 0 + 0.4 3x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 3x + x2 = 0.4 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.4 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.4 + 2.25 Combine like terms: 0.4 + 2.25 = 2.65 2.25 + 3x + x2 = 2.65 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.65 Calculate the square root of the right side: 1.62788206 Break this problem into two subproblems by setting (x + 1.5) equal to 1.62788206 and -1.62788206.Subproblem 1
x + 1.5 = 1.62788206 Simplifying x + 1.5 = 1.62788206 Reorder the terms: 1.5 + x = 1.62788206 Solving 1.5 + x = 1.62788206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.62788206 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.62788206 + -1.5 x = 1.62788206 + -1.5 Combine like terms: 1.62788206 + -1.5 = 0.12788206 x = 0.12788206 Simplifying x = 0.12788206Subproblem 2
x + 1.5 = -1.62788206 Simplifying x + 1.5 = -1.62788206 Reorder the terms: 1.5 + x = -1.62788206 Solving 1.5 + x = -1.62788206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.62788206 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.62788206 + -1.5 x = -1.62788206 + -1.5 Combine like terms: -1.62788206 + -1.5 = -3.12788206 x = -3.12788206 Simplifying x = -3.12788206Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12788206, -3.12788206}
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