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Simplifying 7x + -3 = 4x2 + 5(x + -2) Reorder the terms: -3 + 7x = 4x2 + 5(x + -2) Reorder the terms: -3 + 7x = 4x2 + 5(-2 + x) -3 + 7x = 4x2 + (-2 * 5 + x * 5) -3 + 7x = 4x2 + (-10 + 5x) Reorder the terms: -3 + 7x = -10 + 5x + 4x2 Solving -3 + 7x = -10 + 5x + 4x2 Solving for variable 'x'. Reorder the terms: -3 + 10 + 7x + -5x + -4x2 = -10 + 5x + 4x2 + 10 + -5x + -4x2 Combine like terms: -3 + 10 = 7 7 + 7x + -5x + -4x2 = -10 + 5x + 4x2 + 10 + -5x + -4x2 Combine like terms: 7x + -5x = 2x 7 + 2x + -4x2 = -10 + 5x + 4x2 + 10 + -5x + -4x2 Reorder the terms: 7 + 2x + -4x2 = -10 + 10 + 5x + -5x + 4x2 + -4x2 Combine like terms: -10 + 10 = 0 7 + 2x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2 7 + 2x + -4x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 7 + 2x + -4x2 = 0 + 4x2 + -4x2 7 + 2x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 7 + 2x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -0.5x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -0.5x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -0.5x + x2 = 0 + 1.75 -0.5x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -0.5x + x2 = 1.75 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.75 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.75 + 0.0625 Combine like terms: 1.75 + 0.0625 = 1.8125 0.0625 + -0.5x + x2 = 1.8125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (x + -0.25) equal to 1.346291202 and -1.346291202.Subproblem 1
x + -0.25 = 1.346291202 Simplifying x + -0.25 = 1.346291202 Reorder the terms: -0.25 + x = 1.346291202 Solving -0.25 + x = 1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.346291202 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.346291202 + 0.25 x = 1.346291202 + 0.25 Combine like terms: 1.346291202 + 0.25 = 1.596291202 x = 1.596291202 Simplifying x = 1.596291202Subproblem 2
x + -0.25 = -1.346291202 Simplifying x + -0.25 = -1.346291202 Reorder the terms: -0.25 + x = -1.346291202 Solving -0.25 + x = -1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.346291202 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.346291202 + 0.25 x = -1.346291202 + 0.25 Combine like terms: -1.346291202 + 0.25 = -1.096291202 x = -1.096291202 Simplifying x = -1.096291202Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.596291202, -1.096291202}
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