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Simplifying 4x2 + -16 + -4 = -1x2 + 3x Reorder the terms: -16 + -4 + 4x2 = -1x2 + 3x Combine like terms: -16 + -4 = -20 -20 + 4x2 = -1x2 + 3x Reorder the terms: -20 + 4x2 = 3x + -1x2 Solving -20 + 4x2 = 3x + -1x2 Solving for variable 'x'. Reorder the terms: -20 + -3x + 4x2 + x2 = 3x + -1x2 + -3x + x2 Combine like terms: 4x2 + x2 = 5x2 -20 + -3x + 5x2 = 3x + -1x2 + -3x + x2 Reorder the terms: -20 + -3x + 5x2 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 -20 + -3x + 5x2 = 0 + -1x2 + x2 -20 + -3x + 5x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -20 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -0.6x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.6x + x2 = 0 + 4 -0.6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.6x + x2 = 4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 4 + 0.09 Combine like terms: 4 + 0.09 = 4.09 0.09 + -0.6x + x2 = 4.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + -0.3) equal to 2.022374842 and -2.022374842.Subproblem 1
x + -0.3 = 2.022374842 Simplifying x + -0.3 = 2.022374842 Reorder the terms: -0.3 + x = 2.022374842 Solving -0.3 + x = 2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 2.022374842 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 2.022374842 + 0.3 x = 2.022374842 + 0.3 Combine like terms: 2.022374842 + 0.3 = 2.322374842 x = 2.322374842 Simplifying x = 2.322374842Subproblem 2
x + -0.3 = -2.022374842 Simplifying x + -0.3 = -2.022374842 Reorder the terms: -0.3 + x = -2.022374842 Solving -0.3 + x = -2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -2.022374842 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -2.022374842 + 0.3 x = -2.022374842 + 0.3 Combine like terms: -2.022374842 + 0.3 = -1.722374842 x = -1.722374842 Simplifying x = -1.722374842Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.322374842, -1.722374842}
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