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Simplifying (10x2 + -4x + -21) + (7x2 + -4) = 0 Reorder the terms: (-21 + -4x + 10x2) + (7x2 + -4) = 0 Remove parenthesis around (-21 + -4x + 10x2) -21 + -4x + 10x2 + (7x2 + -4) = 0 Reorder the terms: -21 + -4x + 10x2 + (-4 + 7x2) = 0 Remove parenthesis around (-4 + 7x2) -21 + -4x + 10x2 + -4 + 7x2 = 0 Reorder the terms: -21 + -4 + -4x + 10x2 + 7x2 = 0 Combine like terms: -21 + -4 = -25 -25 + -4x + 10x2 + 7x2 = 0 Combine like terms: 10x2 + 7x2 = 17x2 -25 + -4x + 17x2 = 0 Solving -25 + -4x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -1.470588235 + -0.2352941176x + x2 = 0 Move the constant term to the right: Add '1.470588235' to each side of the equation. -1.470588235 + -0.2352941176x + 1.470588235 + x2 = 0 + 1.470588235 Reorder the terms: -1.470588235 + 1.470588235 + -0.2352941176x + x2 = 0 + 1.470588235 Combine like terms: -1.470588235 + 1.470588235 = 0.000000000 0.000000000 + -0.2352941176x + x2 = 0 + 1.470588235 -0.2352941176x + x2 = 0 + 1.470588235 Combine like terms: 0 + 1.470588235 = 1.470588235 -0.2352941176x + x2 = 1.470588235 The x term is -0.2352941176x. Take half its coefficient (-0.1176470588). Square it (0.01384083044) and add it to both sides. Add '0.01384083044' to each side of the equation. -0.2352941176x + 0.01384083044 + x2 = 1.470588235 + 0.01384083044 Reorder the terms: 0.01384083044 + -0.2352941176x + x2 = 1.470588235 + 0.01384083044 Combine like terms: 1.470588235 + 0.01384083044 = 1.48442906544 0.01384083044 + -0.2352941176x + x2 = 1.48442906544 Factor a perfect square on the left side: (x + -0.1176470588)(x + -0.1176470588) = 1.48442906544 Calculate the square root of the right side: 1.218371481 Break this problem into two subproblems by setting (x + -0.1176470588) equal to 1.218371481 and -1.218371481.Subproblem 1
x + -0.1176470588 = 1.218371481 Simplifying x + -0.1176470588 = 1.218371481 Reorder the terms: -0.1176470588 + x = 1.218371481 Solving -0.1176470588 + x = 1.218371481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1176470588' to each side of the equation. -0.1176470588 + 0.1176470588 + x = 1.218371481 + 0.1176470588 Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000 0.0000000000 + x = 1.218371481 + 0.1176470588 x = 1.218371481 + 0.1176470588 Combine like terms: 1.218371481 + 0.1176470588 = 1.3360185398 x = 1.3360185398 Simplifying x = 1.3360185398Subproblem 2
x + -0.1176470588 = -1.218371481 Simplifying x + -0.1176470588 = -1.218371481 Reorder the terms: -0.1176470588 + x = -1.218371481 Solving -0.1176470588 + x = -1.218371481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1176470588' to each side of the equation. -0.1176470588 + 0.1176470588 + x = -1.218371481 + 0.1176470588 Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000 0.0000000000 + x = -1.218371481 + 0.1176470588 x = -1.218371481 + 0.1176470588 Combine like terms: -1.218371481 + 0.1176470588 = -1.1007244222 x = -1.1007244222 Simplifying x = -1.1007244222Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3360185398, -1.1007244222}
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