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Simplifying x2 + -1(x + -4) + -21 = 0 Reorder the terms: x2 + -1(-4 + x) + -21 = 0 x2 + (-4 * -1 + x * -1) + -21 = 0 x2 + (4 + -1x) + -21 = 0 Reorder the terms: 4 + -21 + -1x + x2 = 0 Combine like terms: 4 + -21 = -17 -17 + -1x + x2 = 0 Solving -17 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -1x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -1x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1x + x2 = 0 + 17 -1x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -1x + x2 = 17 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 17 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 17 + 0.25 Combine like terms: 17 + 0.25 = 17.25 0.25 + -1x + x2 = 17.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + -0.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + -0.5 = 4.153311931 Simplifying x + -0.5 = 4.153311931 Reorder the terms: -0.5 + x = 4.153311931 Solving -0.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.153311931 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.153311931 + 0.5 x = 4.153311931 + 0.5 Combine like terms: 4.153311931 + 0.5 = 4.653311931 x = 4.653311931 Simplifying x = 4.653311931Subproblem 2
x + -0.5 = -4.153311931 Simplifying x + -0.5 = -4.153311931 Reorder the terms: -0.5 + x = -4.153311931 Solving -0.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.153311931 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.153311931 + 0.5 x = -4.153311931 + 0.5 Combine like terms: -4.153311931 + 0.5 = -3.653311931 x = -3.653311931 Simplifying x = -3.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.653311931, -3.653311931}
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