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Simplifying 4(x2 + -3) + x(x + 1) = 0 Reorder the terms: 4(-3 + x2) + x(x + 1) = 0 (-3 * 4 + x2 * 4) + x(x + 1) = 0 (-12 + 4x2) + x(x + 1) = 0 Reorder the terms: -12 + 4x2 + x(1 + x) = 0 -12 + 4x2 + (1 * x + x * x) = 0 -12 + 4x2 + (1x + x2) = 0 Reorder the terms: -12 + 1x + 4x2 + x2 = 0 Combine like terms: 4x2 + x2 = 5x2 -12 + 1x + 5x2 = 0 Solving -12 + 1x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 0.2x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.2x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.2x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.2x + x2 = 0 + 2.4 0.2x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 0.2x + x2 = 2.4 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 2.4 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 2.4 + 0.01 Combine like terms: 2.4 + 0.01 = 2.41 0.01 + 0.2x + x2 = 2.41 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 2.41 Calculate the square root of the right side: 1.55241747 Break this problem into two subproblems by setting (x + 0.1) equal to 1.55241747 and -1.55241747.Subproblem 1
x + 0.1 = 1.55241747 Simplifying x + 0.1 = 1.55241747 Reorder the terms: 0.1 + x = 1.55241747 Solving 0.1 + x = 1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.55241747 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.55241747 + -0.1 x = 1.55241747 + -0.1 Combine like terms: 1.55241747 + -0.1 = 1.45241747 x = 1.45241747 Simplifying x = 1.45241747Subproblem 2
x + 0.1 = -1.55241747 Simplifying x + 0.1 = -1.55241747 Reorder the terms: 0.1 + x = -1.55241747 Solving 0.1 + x = -1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.55241747 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.55241747 + -0.1 x = -1.55241747 + -0.1 Combine like terms: -1.55241747 + -0.1 = -1.65241747 x = -1.65241747 Simplifying x = -1.65241747Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.45241747, -1.65241747}
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