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Simplifying 0.7x2 + -4.2x + -0.7 = 0 Reorder the terms: -0.7 + -4.2x + 0.7x2 = 0 Solving -0.7 + -4.2x + 0.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.7 the coefficient of the squared term: Divide each side by '0.7'. -1 + -6x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -6x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6x + x2 = 0 + 1 -6x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6x + x2 = 1 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 1 + 9 Reorder the terms: 9 + -6x + x2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6x + x2 = 10 Factor a perfect square on the left side: (x + -3)(x + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -3 = 3.16227766 Simplifying x + -3 = 3.16227766 Reorder the terms: -3 + x = 3.16227766 Solving -3 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.16227766 + 3 x = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 x = 6.16227766 Simplifying x = 6.16227766Subproblem 2
x + -3 = -3.16227766 Simplifying x + -3 = -3.16227766 Reorder the terms: -3 + x = -3.16227766 Solving -3 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.16227766 + 3 x = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 x = -0.16227766 Simplifying x = -0.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.16227766, -0.16227766}
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