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Simplifying 4x2 + -6 + -9x2 + 10 + 7x = 0 Reorder the terms: -6 + 10 + 7x + 4x2 + -9x2 = 0 Combine like terms: -6 + 10 = 4 4 + 7x + 4x2 + -9x2 = 0 Combine like terms: 4x2 + -9x2 = -5x2 4 + 7x + -5x2 = 0 Solving 4 + 7x + -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'. -0.8 + -1.4x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.4x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.4x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.4x + x2 = 0 + 0.8 -1.4x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.4x + x2 = 0.8 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 0.8 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 0.8 + 0.49 Combine like terms: 0.8 + 0.49 = 1.29 0.49 + -1.4x + x2 = 1.29 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (x + -0.7) equal to 1.135781669 and -1.135781669.Subproblem 1
x + -0.7 = 1.135781669 Simplifying x + -0.7 = 1.135781669 Reorder the terms: -0.7 + x = 1.135781669 Solving -0.7 + x = 1.135781669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.135781669 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.135781669 + 0.7 x = 1.135781669 + 0.7 Combine like terms: 1.135781669 + 0.7 = 1.835781669 x = 1.835781669 Simplifying x = 1.835781669Subproblem 2
x + -0.7 = -1.135781669 Simplifying x + -0.7 = -1.135781669 Reorder the terms: -0.7 + x = -1.135781669 Solving -0.7 + x = -1.135781669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.135781669 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.135781669 + 0.7 x = -1.135781669 + 0.7 Combine like terms: -1.135781669 + 0.7 = -0.435781669 x = -0.435781669 Simplifying x = -0.435781669Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.835781669, -0.435781669}
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