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Simplifying 2x2 + (-4) + 7x2 + (-4x) + (-7) = 0 2x2 + -4 + 7x2 + (-4x) + (-7) = 0 2x2 + -4 + 7x2 + (-4x) + -7 = 0 Reorder the terms: -4 + -7 + (-4x) + 2x2 + 7x2 = 0 Combine like terms: -4 + -7 = -11 -11 + (-4x) + 2x2 + 7x2 = 0 Combine like terms: 2x2 + 7x2 = 9x2 -11 + (-4x) + 9x2 = 0 Solving -11 + (-4x) + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.222222222 + (-0.4444444444x) + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + (-0.4444444444x) + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + (-0.4444444444x) + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + (-0.4444444444x) + x2 = 0 + 1.222222222 (-0.4444444444x) + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 (-0.4444444444x) + x2 = 1.222222222 The x term is (-0.4444444444x). Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. (-0.4444444444x) + 0.04938271604 + x2 = 1.222222222 + 0.04938271604 Reorder the terms: 0.04938271604 + (-0.4444444444x) + x2 = 1.222222222 + 0.04938271604 Combine like terms: 1.222222222 + 0.04938271604 = 1.27160493804 0.04938271604 + (-0.4444444444x) + x2 = 1.27160493804 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 1.27160493804 Calculate the square root of the right side: 1.127654618 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 1.127654618 and -1.127654618.Subproblem 1
x + -0.2222222222 = 1.127654618 Simplifying x + -0.2222222222 = 1.127654618 Reorder the terms: -0.2222222222 + x = 1.127654618 Solving -0.2222222222 + x = 1.127654618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 1.127654618 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 1.127654618 + 0.2222222222 x = 1.127654618 + 0.2222222222 Combine like terms: 1.127654618 + 0.2222222222 = 1.3498768402 x = 1.3498768402 Simplifying x = 1.3498768402Subproblem 2
x + -0.2222222222 = -1.127654618 Simplifying x + -0.2222222222 = -1.127654618 Reorder the terms: -0.2222222222 + x = -1.127654618 Solving -0.2222222222 + x = -1.127654618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -1.127654618 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -1.127654618 + 0.2222222222 x = -1.127654618 + 0.2222222222 Combine like terms: -1.127654618 + 0.2222222222 = -0.9054323958 x = -0.9054323958 Simplifying x = -0.9054323958Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3498768402, -0.9054323958}
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