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Simplifying 10x2 + -7 = 4x Reorder the terms: -7 + 10x2 = 4x Solving -7 + 10x2 = 4x Solving for variable 'x'. Reorder the terms: -7 + -4x + 10x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -7 + -4x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -0.4x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + -0.4x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -0.4x + x2 = 0 + 0.7 -0.4x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 -0.4x + x2 = 0.7 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.7 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.7 + 0.04 Combine like terms: 0.7 + 0.04 = 0.74 0.04 + -0.4x + x2 = 0.74 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.74 Calculate the square root of the right side: 0.860232527 Break this problem into two subproblems by setting (x + -0.2) equal to 0.860232527 and -0.860232527.Subproblem 1
x + -0.2 = 0.860232527 Simplifying x + -0.2 = 0.860232527 Reorder the terms: -0.2 + x = 0.860232527 Solving -0.2 + x = 0.860232527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.860232527 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.860232527 + 0.2 x = 0.860232527 + 0.2 Combine like terms: 0.860232527 + 0.2 = 1.060232527 x = 1.060232527 Simplifying x = 1.060232527Subproblem 2
x + -0.2 = -0.860232527 Simplifying x + -0.2 = -0.860232527 Reorder the terms: -0.2 + x = -0.860232527 Solving -0.2 + x = -0.860232527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.860232527 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.860232527 + 0.2 x = -0.860232527 + 0.2 Combine like terms: -0.860232527 + 0.2 = -0.660232527 x = -0.660232527 Simplifying x = -0.660232527Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.060232527, -0.660232527}
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