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Simplifying (-4x2 + 4x) + -1(6x2 + 7x + -3) = 0 Reorder the terms: (4x + -4x2) + -1(6x2 + 7x + -3) = 0 Remove parenthesis around (4x + -4x2) 4x + -4x2 + -1(6x2 + 7x + -3) = 0 Reorder the terms: 4x + -4x2 + -1(-3 + 7x + 6x2) = 0 4x + -4x2 + (-3 * -1 + 7x * -1 + 6x2 * -1) = 0 4x + -4x2 + (3 + -7x + -6x2) = 0 Reorder the terms: 3 + 4x + -7x + -4x2 + -6x2 = 0 Combine like terms: 4x + -7x = -3x 3 + -3x + -4x2 + -6x2 = 0 Combine like terms: -4x2 + -6x2 = -10x2 3 + -3x + -10x2 = 0 Solving 3 + -3x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.3 + 0.3x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.3x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.3x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.3x + x2 = 0.0 + 0.3 0.3x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 0.3x + x2 = 0.3 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 0.3 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.3 + 0.0225 Combine like terms: 0.3 + 0.0225 = 0.3225 0.0225 + 0.3x + x2 = 0.3225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.3225 Calculate the square root of the right side: 0.567890835 Break this problem into two subproblems by setting (x + 0.15) equal to 0.567890835 and -0.567890835.Subproblem 1
x + 0.15 = 0.567890835 Simplifying x + 0.15 = 0.567890835 Reorder the terms: 0.15 + x = 0.567890835 Solving 0.15 + x = 0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.567890835 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.567890835 + -0.15 x = 0.567890835 + -0.15 Combine like terms: 0.567890835 + -0.15 = 0.417890835 x = 0.417890835 Simplifying x = 0.417890835Subproblem 2
x + 0.15 = -0.567890835 Simplifying x + 0.15 = -0.567890835 Reorder the terms: 0.15 + x = -0.567890835 Solving 0.15 + x = -0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.567890835 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.567890835 + -0.15 x = -0.567890835 + -0.15 Combine like terms: -0.567890835 + -0.15 = -0.717890835 x = -0.717890835 Simplifying x = -0.717890835Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.417890835, -0.717890835}
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