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Simplifying 3x2 + -5x + -4 = -7x2 + 2x + 1 Reorder the terms: -4 + -5x + 3x2 = -7x2 + 2x + 1 Reorder the terms: -4 + -5x + 3x2 = 1 + 2x + -7x2 Solving -4 + -5x + 3x2 = 1 + 2x + -7x2 Solving for variable 'x'. Reorder the terms: -4 + -1 + -5x + -2x + 3x2 + 7x2 = 1 + 2x + -7x2 + -1 + -2x + 7x2 Combine like terms: -4 + -1 = -5 -5 + -5x + -2x + 3x2 + 7x2 = 1 + 2x + -7x2 + -1 + -2x + 7x2 Combine like terms: -5x + -2x = -7x -5 + -7x + 3x2 + 7x2 = 1 + 2x + -7x2 + -1 + -2x + 7x2 Combine like terms: 3x2 + 7x2 = 10x2 -5 + -7x + 10x2 = 1 + 2x + -7x2 + -1 + -2x + 7x2 Reorder the terms: -5 + -7x + 10x2 = 1 + -1 + 2x + -2x + -7x2 + 7x2 Combine like terms: 1 + -1 = 0 -5 + -7x + 10x2 = 0 + 2x + -2x + -7x2 + 7x2 -5 + -7x + 10x2 = 2x + -2x + -7x2 + 7x2 Combine like terms: 2x + -2x = 0 -5 + -7x + 10x2 = 0 + -7x2 + 7x2 -5 + -7x + 10x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -5 + -7x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + -0.7x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.7x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.7x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.7x + x2 = 0.0 + 0.5 -0.7x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -0.7x + x2 = 0.5 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = 0.5 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 0.5 + 0.1225 Combine like terms: 0.5 + 0.1225 = 0.6225 0.1225 + -0.7x + x2 = 0.6225 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 0.6225 Calculate the square root of the right side: 0.788986692 Break this problem into two subproblems by setting (x + -0.35) equal to 0.788986692 and -0.788986692.Subproblem 1
x + -0.35 = 0.788986692 Simplifying x + -0.35 = 0.788986692 Reorder the terms: -0.35 + x = 0.788986692 Solving -0.35 + x = 0.788986692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 0.788986692 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.788986692 + 0.35 x = 0.788986692 + 0.35 Combine like terms: 0.788986692 + 0.35 = 1.138986692 x = 1.138986692 Simplifying x = 1.138986692Subproblem 2
x + -0.35 = -0.788986692 Simplifying x + -0.35 = -0.788986692 Reorder the terms: -0.35 + x = -0.788986692 Solving -0.35 + x = -0.788986692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -0.788986692 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -0.788986692 + 0.35 x = -0.788986692 + 0.35 Combine like terms: -0.788986692 + 0.35 = -0.438986692 x = -0.438986692 Simplifying x = -0.438986692Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.138986692, -0.438986692}
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