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Simplifying 4x2 + -4.2x + -1.3 = 0 Reorder the terms: -1.3 + -4.2x + 4x2 = 0 Solving -1.3 + -4.2x + 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'. -0.325 + -1.05x + x2 = 0 Move the constant term to the right: Add '0.325' to each side of the equation. -0.325 + -1.05x + 0.325 + x2 = 0 + 0.325 Reorder the terms: -0.325 + 0.325 + -1.05x + x2 = 0 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + -1.05x + x2 = 0 + 0.325 -1.05x + x2 = 0 + 0.325 Combine like terms: 0 + 0.325 = 0.325 -1.05x + x2 = 0.325 The x term is -1.05x. Take half its coefficient (-0.525). Square it (0.275625) and add it to both sides. Add '0.275625' to each side of the equation. -1.05x + 0.275625 + x2 = 0.325 + 0.275625 Reorder the terms: 0.275625 + -1.05x + x2 = 0.325 + 0.275625 Combine like terms: 0.325 + 0.275625 = 0.600625 0.275625 + -1.05x + x2 = 0.600625 Factor a perfect square on the left side: (x + -0.525)(x + -0.525) = 0.600625 Calculate the square root of the right side: 0.775 Break this problem into two subproblems by setting (x + -0.525) equal to 0.775 and -0.775.Subproblem 1
x + -0.525 = 0.775 Simplifying x + -0.525 = 0.775 Reorder the terms: -0.525 + x = 0.775 Solving -0.525 + x = 0.775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + x = 0.775 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + x = 0.775 + 0.525 x = 0.775 + 0.525 Combine like terms: 0.775 + 0.525 = 1.3 x = 1.3 Simplifying x = 1.3Subproblem 2
x + -0.525 = -0.775 Simplifying x + -0.525 = -0.775 Reorder the terms: -0.525 + x = -0.775 Solving -0.525 + x = -0.775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + x = -0.775 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + x = -0.775 + 0.525 x = -0.775 + 0.525 Combine like terms: -0.775 + 0.525 = -0.25 x = -0.25 Simplifying x = -0.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3, -0.25}
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