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Simplifying x2 + -14x + 42 = 3 Reorder the terms: 42 + -14x + x2 = 3 Solving 42 + -14x + x2 = 3 Solving for variable 'x'. Reorder the terms: 42 + -3 + -14x + x2 = 3 + -3 Combine like terms: 42 + -3 = 39 39 + -14x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 39 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + -14x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + -14x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -14x + x2 = 0 + -39 -14x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 -14x + x2 = -39 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -39 + 49 Reorder the terms: 49 + -14x + x2 = -39 + 49 Combine like terms: -39 + 49 = 10 49 + -14x + x2 = 10 Factor a perfect square on the left side: (x + -7)(x + -7) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -7) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -7 = 3.16227766 Simplifying x + -7 = 3.16227766 Reorder the terms: -7 + x = 3.16227766 Solving -7 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 3.16227766 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.16227766 + 7 x = 3.16227766 + 7 Combine like terms: 3.16227766 + 7 = 10.16227766 x = 10.16227766 Simplifying x = 10.16227766Subproblem 2
x + -7 = -3.16227766 Simplifying x + -7 = -3.16227766 Reorder the terms: -7 + x = -3.16227766 Solving -7 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -3.16227766 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.16227766 + 7 x = -3.16227766 + 7 Combine like terms: -3.16227766 + 7 = 3.83772234 x = 3.83772234 Simplifying x = 3.83772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.16227766, 3.83772234}
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